Pith. sign in

Paper Citation Record · LEDGER

A Minkowski problem for $\alpha$-concave functions via optimal transport

As of 18 August 2026, this Paper Citation Record lists 63 of 63 outbound references and 1 inbound Pith citation observation for arXiv:2506.14735.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.14735 v2

Coverage vector

measured 63 of 63 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T20:01:34.423751Z

measured 64 of 64 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T17:28:49.682827Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-15T17:28:49.884655Z

Reference resolution

63 of 63 outbound references displayed

  • verified exact0
  • verified fuzzy30
  • unresolved33
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1dbf2c59-6166-4f88-aa80-aedb230e3522 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:35.096862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.209775Z digest=sha256:4fd36758b4286fc94f86ab8a68a7dd33707d77dc26eaacad8dad479b94e53414

Observation 6d32ad53-2bce-4726-9636-1238ed107317 · outbound

This paper cites H., Villa, R.:Rogers-Shephard and local Loomis–Whitney type inequalities.

A Minkowski problem for $\alpha$-concave functions via optimal transport H., Villa, R.:Rogers-Shephard and local Loomis–Whitney type inequalities

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:35.086722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.214181Z digest=sha256:2d7525578784562dec5dffd240f6f84ade270d8a6aa5e0eb123a938483488d90

Observation 41cb432e-ab58-4b12-8b09-038574142e8b · outbound

This paper cites H., Villa, R.:Rogers–Shephard inequality for log- concave functions.

A Minkowski problem for $\alpha$-concave functions via optimal transport H., Villa, R.:Rogers–Shephard inequality for log- concave functions

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:35.076285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.218068Z digest=sha256:f293403685248b1e40545b2f419f9f4af16e001dc3f88da0702e07c6f7eeb038

Observation 78fb0341-2451-4812-bcbd-2fc58e911a2a · outbound

This paper cites H., Villa, R.:John’s Ellipsoid and the Integral Ratio of a Log-Concave Function.

A Minkowski problem for $\alpha$-concave functions via optimal transport H., Villa, R.:John’s Ellipsoid and the Integral Ratio of a Log-Concave Function

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:35.065863Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.221910Z digest=sha256:de267ab5e1b3ed8a6643aabcfd905372661f972a28f9ef47e57ea89b295c83cd

Observation b69ec3eb-5724-41b2-a136-48f89f308db6 · outbound

This paper cites 51, 33-48 (2004).

A Minkowski problem for $\alpha$-concave functions via optimal transport 51, 33-48 (2004)

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:35.054683Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.225550Z digest=sha256:60ec3ba6e6299e3c8d5a30e9ea29143da7e5e70932aa5f1eb339220f1a1e0f95

Observation b83bd834-8246-4656-92b9-fe3bc496e509 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:35.043821Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.229134Z digest=sha256:d0de006826f2d26f26ed7637b6cee89929e1fa1795894c31c66b09f56474dacd

Observation 8e0f8a53-64ab-4c85-8599-ac29d94d85f0 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:35.033144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.232930Z digest=sha256:bb83e5887179c978b0931187d73ef3feb4b40153ba38e7deb753dce018521696

Observation e78d6671-a436-4d98-afe6-d99b407ce61e · outbound

This paper cites J., Colesanti, A., Yang, D.: The Lp-Minkowski problem for −n < p <1.

A Minkowski problem for $\alpha$-concave functions via optimal transport J., Colesanti, A., Yang, D.: The Lp-Minkowski problem for −n < p <1

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:35.021188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.236383Z digest=sha256:41a948fd098bbc4060c2e080e18b29f44ca7b0c371fd29376cf8db83343ff625

Observation e264d5d5-56cc-4d85-91a6-87f832ff86c2 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:35.010101Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.240168Z digest=sha256:a31b21433f77852bbf31ea1324c6a703c5c4b4abd421d76021a842663c7849d2

Observation f01ac56e-456a-4ac7-b393-03102d0f206d · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.999283Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.243723Z digest=sha256:1a188d1ddbd04ed464ffce3853c587cde0d7155cfbc2aa5bb4106448f59c32f7

Observation b0c3174d-f6ef-44a4-8827-b2182fa6e338 · outbound

This paper cites J., Lutwak, E., Yang, D., Zhang, G.:The logarithmic Minkowski problem.

A Minkowski problem for $\alpha$-concave functions via optimal transport J., Lutwak, E., Yang, D., Zhang, G.:The logarithmic Minkowski problem

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.988744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.247216Z digest=sha256:a25d30b3976d95cb798588d0c140d9cb77db18ff45ca4df9ebac03e97bf0792f

Observation 8f1e9a0e-3860-443a-9730-70c70797ee68 · outbound

This paper cites J., Lutwak, E., Yang, D., Zhang, G., Zhao, Y.:The Gauss Image Problem.

A Minkowski problem for $\alpha$-concave functions via optimal transport J., Lutwak, E., Yang, D., Zhang, G., Zhao, Y.:The Gauss Image Problem

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.978413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.251208Z digest=sha256:0d608ed1dd44c6a8680f7a7f42b544c5f1f7134b9f6d240ad8669314bf37724d

Observation 7224dd24-dd47-4f17-8ae4-8e6cba7104c6 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.968135Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.254758Z digest=sha256:5a15c2c97e50af77b14f98ce3b71e44122d518509f6f828aa509d014f38b57fd

Observation 431b5a42-d29b-40ca-8d6d-686a939c0c48 · outbound

This paper cites J., Lieb, E.

A Minkowski problem for $\alpha$-concave functions via optimal transport J., Lieb, E

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.957634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.258026Z digest=sha256:c8e556702fb7845a2b9288d7ade0d0ff51446af26e5dad5409f5e39c62b0fdf2

Observation c287aac7-d798-487c-b47f-ea66b8ea0a7f · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.947219Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.260980Z digest=sha256:b0441df1d88a418dc8d1761d343a96ba9983fb0265c83d7340dd3b5ee81d7b8e

Observation 3b63078c-a3b6-444d-ad5e-3568bb9faa9d · outbound

This paper cites M.:Functional Versions ofLp-Affine Surface Area and Entropy Inequalities.

A Minkowski problem for $\alpha$-concave functions via optimal transport M.:Functional Versions ofLp-Affine Surface Area and Entropy Inequalities

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.936422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.264025Z digest=sha256:967636cf5405a0fd9970186d5cf72c52b1fe74bfa3d9742dec4e205b80d567fd

Observation df6d71b6-2a2b-43da-a67d-37f81b772dc9 · outbound

This paper cites M.: Divergence for s-concave and log concave functions.

A Minkowski problem for $\alpha$-concave functions via optimal transport M.: Divergence for s-concave and log concave functions

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.925406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.266654Z digest=sha256:9f0777a8aa4e1b96e8c53dfce541764a43ea7d6fc0a52d34f8573ce2f5118f76

Observation db17ed7c-a452-41dc-9092-e878540b5b5e · outbound

This paper cites M.: Mixed f-divergence and inequalities for log-concave functions.

A Minkowski problem for $\alpha$-concave functions via optimal transport M.: Mixed f-divergence and inequalities for log-concave functions

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.914537Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.269518Z digest=sha256:50778d92ae0fcd29ef115113ef281e897bd9e968cf38991ce0aa65b085311965

Observation 4739e989-21d2-4aac-8ebc-1721860a6ea4 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.903418Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.273022Z digest=sha256:ef3000ad7bc3f16398bb7602f673940800fe6c1e51fed353f11ae9ec570e954d

Observation 3aa65332-5380-46be-9de3-438e8fbbf079 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.893900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.276484Z digest=sha256:2a38c9e1d8627f2da9dd690dadeab7a26b023d505dcc9de67aac1afe531d3f1d

Observation d6511d0e-feb9-41ef-91a8-c9ffffbc9e12 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.884466Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.280013Z digest=sha256:41561f9e013ae39cd5e8fdd81c2c98a265c905c9a0bfe0f8936aeb029052d166

Observation 74588758-13eb-47d6-af59-91922fee82d4 · outbound

This paper cites Cambridge University Press, Cambridge, (2019).

A Minkowski problem for $\alpha$-concave functions via optimal transport Cambridge University Press, Cambridge, (2019)

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.874129Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.283424Z digest=sha256:e5abd834c1a2b2aff7b128b06daf1c54d14dadbf5c4fc6ab0d229e8a195491b3

Observation 1c782833-6005-4b18-93a5-2b41e09b9430 · outbound

This paper cites On the functional Minkowski problem.

A Minkowski problem for $\alpha$-concave functions via optimal transport On the functional Minkowski problem

Reference 23

Resolution
unresolved
no resolver link, observed 2026-08-15T20:01:34.286738Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T20:01:34.286738Z digest=sha256:a453a611f5cd558e8c1aa997fec1d1c24869d3b0775379dce367d89747732974

Observation 9d216271-2d1f-4d6f-ac51-5b63a6da19bd · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.864209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.290380Z digest=sha256:54ed521c238f07a9574fdcbfe62f10cb69ca4b5aed32dfd577297f63042e0379

Observation f02d848f-f384-49d1-bd9b-926d1c4818df · outbound

This paper cites The Riesz $\alpha$-energy of log-concave functions and related Minkowski problem.

A Minkowski problem for $\alpha$-concave functions via optimal transport The Riesz $\alpha$-energy of log-concave functions and related Minkowski problem

Reference 25

Resolution
unresolved
no resolver link, observed 2026-08-15T20:01:34.293718Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T20:01:34.293718Z digest=sha256:9122a17cddd4005f3d0a25360b1f1cd0ec3d68aa558e59f5d52544bfe959772f

Observation 68bbda01-1ce9-4f02-9992-0885172b0418 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.854325Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.297350Z digest=sha256:4f873ba99348000ef3d9c63dc1e0803bcd709bd28348297db2b011712bb2555e

Observation 054a599a-820b-4ea9-adaa-30765c5eb665 · outbound

This paper cites EMS Press, Berlin, (2021).

A Minkowski problem for $\alpha$-concave functions via optimal transport EMS Press, Berlin, (2021)

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.843736Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.300468Z digest=sha256:7946069fcae7345cec4188cf1458b45a73c23038cd891366a4b55e47facf9514

Observation 64e20eb2-2ae0-4a55-b4ab-552cd850b604 · outbound

This paper cites B.: Real Analysis: Modern Techniques and Their Applications.

A Minkowski problem for $\alpha$-concave functions via optimal transport B.: Real Analysis: Modern Techniques and Their Applications

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.833591Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.303942Z digest=sha256:1eebe3db0e8b8a16834e58551c34d599f5ca13e0678f409db2a3577c16f0e326

Observation b26d2d97-2cd4-48c2-a4dc-132233725ddb · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.823690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.307286Z digest=sha256:2bb11fbb729a4747d13ff21e3c86d913ad9e6dbaef4911918c6b3f913a04fc36

Observation d0d022ab-4881-4c6d-acf9-cecec50df4e8 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.813314Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.310330Z digest=sha256:a807ab6b133efec31de0f410c5b8a9eecd7c8f16fae37b970b106cd8e91dcd82

Observation eaec1a21-aafd-45c1-ba4d-6548d3665efe · outbound

This paper cites J.: The geometry of optimal transportation.

A Minkowski problem for $\alpha$-concave functions via optimal transport J.: The geometry of optimal transportation

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.803350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.313575Z digest=sha256:592a0f65d271d4c8026e67860706287a91ca8e1f64eb07fbc48bd7d7a1879818

Observation 7ef6a831-c41a-4a21-8b44-65f626b4abff · outbound

This paper cites J., Hug, D., Weil, W., Xing, S., Ye, D.: General volumes in the Orlicz-Brunn–Minkowski theory and a related Minkowski problem I.

A Minkowski problem for $\alpha$-concave functions via optimal transport J., Hug, D., Weil, W., Xing, S., Ye, D.: General volumes in the Orlicz-Brunn–Minkowski theory and a related Minkowski problem I

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.793341Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.316777Z digest=sha256:d8531dcb3f81e7000e7b6f6ca005b0047cd8623155d22a4df9f08cdf9b5c936b

Observation 0f91e70e-ec7f-4b5e-9ba4-ee535f6af2de · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 33

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.783565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.319983Z digest=sha256:d908867c68519dfebceae8e65e97a3529b8f478ec4f8da625a8cbdbaa38f3796

Observation f83a8064-4447-4732-9cbd-af5b5bc3344a · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 34

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.774406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.323432Z digest=sha256:8b96291b07b594b50d676907837f5653ab4afa6c18208bebeeec1691006a069e

Observation 54ed2104-b0b8-4923-8e80-35ef1000f791 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 35

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.764892Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.326696Z digest=sha256:e457c3a8fade9b865f1a97751dce62b8f7c010e5c7ccb1791c847ac0877323d6

Observation 46674ae5-1e6d-44a6-8d66-54f43795073e · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 36

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.754919Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.330272Z digest=sha256:7f28f9c078e30279440610cab4dc5e69f2f7b34918893943e9cc856f007d70b2

Observation e936c503-28d8-4555-8d0d-7d03a5270ca1 · outbound

This paper cites Journal of Convex Analysis.

A Minkowski problem for $\alpha$-concave functions via optimal transport Journal of Convex Analysis

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.742818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.333776Z digest=sha256:1af7833ed7e89691e43d08ffc36a67a032f86d6d5ba82fb33a7185474b691bc8

Observation bc5c1bf5-fdc0-468b-b01a-a71b239932e3 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 38

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.732108Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.337115Z digest=sha256:add8cd75c3bb349718c4b71692305d39bedea5e19c941fe4b6480e39016597a7

Observation 85384088-b909-48a2-91d0-beffc899e682 · outbound

This paper cites D.: Geometry of Log-concave Functions and Measures.

A Minkowski problem for $\alpha$-concave functions via optimal transport D.: Geometry of Log-concave Functions and Measures

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.722002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.340539Z digest=sha256:edb1a28a4282a3cf6aba508d5d618db2d4c2d16c86ee087099c4c00ec1938de3

Observation 1a2f5b9b-dd4c-41fa-9b38-826d0d654a44 · outbound

This paper cites S.: On the optimal mapping of distributions.

A Minkowski problem for $\alpha$-concave functions via optimal transport S.: On the optimal mapping of distributions

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.711412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.344027Z digest=sha256:dd452769aed020dae99ee13015cec37a2e39a2baa3aa2138731a413385fbb6b3

Observation 91c35c98-0a82-4dd9-b923-882b1226de55 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 41

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.701220Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.347647Z digest=sha256:d52be84d2257cad805bda64903d65c48568af8b52d464536fff82f5aea69b865

Observation 01e1fb0e-7634-4196-89c5-25e8f9ada935 · outbound

This paper cites M.: Floating functions.

A Minkowski problem for $\alpha$-concave functions via optimal transport M.: Floating functions

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.690676Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.350966Z digest=sha256:135228d05e1a6d34ebf633188b64355c48d3e7f2e3f20292afa5e681740758ac

Observation 3356c1a2-60a2-4b1a-80d5-e54ba055771f · outbound

This paper cites M.: The L¨ owner Function of a Log-Concave Function.

A Minkowski problem for $\alpha$-concave functions via optimal transport M.: The L¨ owner Function of a Log-Concave Function

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.680352Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.354402Z digest=sha256:a91ce9483908b86616e775c82d13c23293bca7c3eb66daf3c974b5f8c9bfc066

Observation 13d66777-3da1-40a3-bbec-5b34206363d2 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 44

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.669997Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.358014Z digest=sha256:25512269b5c30993ff9daa616262c380c122c4c414f164e3f9b8b1e438e07cd7

Observation 1f48668e-7d35-4742-a2c9-808c036877b8 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 45

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.660089Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.361329Z digest=sha256:f71899e30514fd691a3d3f78544cb7450cd3a38355b7e017b5d207f40b144ed4

Observation b067f036-ca51-4d0d-949a-72b7289901ef · outbound

This paper cites J.: Polar factorization of maps on Riemannian manifolds.

A Minkowski problem for $\alpha$-concave functions via optimal transport J.: Polar factorization of maps on Riemannian manifolds

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.650295Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.364575Z digest=sha256:f3dae7d7177ae18a87277507b80742be70e77c36237f3c08f560cfcd775bb340

Observation f731b2ba-b665-46db-a43c-cd898240f297 · outbound

This paper cites Electron.

A Minkowski problem for $\alpha$-concave functions via optimal transport Electron

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.641097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.368208Z digest=sha256:04882f93ef92fd8dbeab37b3c39df8e603ad0bfdb05d6c4021133c1c42a22d7c

Observation b5cf5f4c-abfe-4dbd-abaf-1edf42dd3ffa · outbound

This paper cites (ed.) Ausgew¨ ahlte Arbeiten zur Zahlentheorie und zur Geometrie: Mit D.

A Minkowski problem for $\alpha$-concave functions via optimal transport (ed.) Ausgew¨ ahlte Arbeiten zur Zahlentheorie und zur Geometrie: Mit D

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.631227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.371601Z digest=sha256:9014eb8535da35cfe65d71a66e0d8af944c737a0ccd3fb832b5c5bb6f4e6fe27

Observation f37b2aee-32de-4cf4-9bed-4996abc927c5 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 49

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.609717Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.379225Z digest=sha256:ec1ed6b8bb94220ad735a91db87ef728545c241cb952d5253aa80a785d8d8905

Observation e197fb18-146f-47ac-acea-c54d744c87c6 · outbound

This paper cites T.: Convex Analysis.

A Minkowski problem for $\alpha$-concave functions via optimal transport T.: Convex Analysis

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.599928Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.382654Z digest=sha256:482c7b84660f7f0d3de643e340974fb2a1c2854d29303c542c3665efa358237a

Observation 9d5a7eda-4d4e-4de9-9a2f-f8949b8e1a76 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 51

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.589775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.386481Z digest=sha256:ef97f67b586723bf43e7eff02f86208e6b93217eab2a57edd64f7cc1771f003e

Observation e8a24578-a47d-4c59-a1d1-2e53d0eec540 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 52

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.579543Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.389803Z digest=sha256:f2ca7e149b7fd5f44d837e550e7dc1a2f74d18ffb215184c9c5324ef47a2afec

Observation 05bcaf6d-dd44-406d-b168-27bf0866f0b6 · outbound

This paper cites In: Eldan, R., Klartag, B., Litvak, A., and Milman, E.

A Minkowski problem for $\alpha$-concave functions via optimal transport In: Eldan, R., Klartag, B., Litvak, A., and Milman, E

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.569778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.393042Z digest=sha256:32d9ffa9c568b648d0fe4bb2696318c99b8d08e0d96933177385a04f7b924b0c

Observation 9d265807-3c7a-4242-b0ad-6564794d1420 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 54

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.559721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.396295Z digest=sha256:fe0375a04ee6860b84a14c52ea262c13c58d53d302b6a5de5e14d5be3b0732ea

Observation 9ccf0722-74ef-40f6-963c-d61ba2ceff7a · outbound

This paper cites Birkh¨ auser/Springer, Cham, (2015).

A Minkowski problem for $\alpha$-concave functions via optimal transport Birkh¨ auser/Springer, Cham, (2015)

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.548697Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.399585Z digest=sha256:7633b3e07b4df06140a745f6e207c669d90f3e60cfa0c83edf75d4c6db39283c

Observation b34ac6bb-ab5b-4603-8062-0b731e853e18 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 56

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.538119Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.403005Z digest=sha256:26dd1faf4f4936a6d3311a603152b09586622df4dae285d2668c65ec795d49e9

Observation 66d035d0-67ce-4879-b558-ff80dd8d9e03 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 57

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.526955Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.406288Z digest=sha256:e2fcec9ae68c41f98f47a539aa2127f6c335d829e2744d6cdad8008e5c701846

Observation 80a87603-b2b1-44d3-a591-8eb1a9930f76 · outbound

This paper cites First variation of functional Wulff shapes.

A Minkowski problem for $\alpha$-concave functions via optimal transport First variation of functional Wulff shapes

Reference 58

Resolution
unresolved
no resolver link, observed 2026-08-15T20:01:34.409642Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T20:01:34.409642Z digest=sha256:7d2f6dd794c6d160ada4b94afc0c4d02a516ce827c220a8289a6db8d44579d35

Observation 70bb6620-f8c3-4dcc-9231-e31fa6228b7a · outbound

This paper cites American Mathematical Society, Providence, RI, (2003).

A Minkowski problem for $\alpha$-concave functions via optimal transport American Mathematical Society, Providence, RI, (2003)

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.517223Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.413596Z digest=sha256:179ead8416bf4a63c9cf202da81d7199ef80190b3691604d91274c1a3911c24a

Observation bba889ec-7ac4-450c-9efd-e0bffe1b33a0 · outbound

This paper cites Springer-Verlag, Berlin, (2009).

A Minkowski problem for $\alpha$-concave functions via optimal transport Springer-Verlag, Berlin, (2009)

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.507185Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.416712Z digest=sha256:6adca6ac7974424169649e7f5be2f16d15349b75e6821f4d19a83f471ce0145e

Observation 767f8b0e-4229-41b9-9113-5f37b7da2d45 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 61

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.496727Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.420145Z digest=sha256:251e62648a4bd16931129138b63627273f2da768310e690b3b5ccd8cd754573d

Observation 74507792-1dd4-41da-849b-13f0eb473935 · outbound

This paper cites an unresolved cited work.

A Minkowski problem for $\alpha$-concave functions via optimal transport Unresolved cited work

Reference 62

Resolution
unresolved
raw_fallback, observed 2026-08-15T20:01:34.485802Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.423751Z digest=sha256:2d0421975c356791690666bfb644183e6ab974405c0c93ff0c267ed54167cd25

Observation dcc4817d-d5b0-45b7-84fe-f29455e2f204 · outbound

This paper cites Springer, Vienna (1989).

A Minkowski problem for $\alpha$-concave functions via optimal transport Springer, Vienna (1989)

Reference 1909

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T20:01:34.620491Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T20:01:34.375602Z digest=sha256:aa9387dbc561fcb236d6785039ca131f6d5c28c3ad0f55c199888a0ba1679b5e

Pith citing papers

Observation 0905cf9a-f6f3-4787-b3f0-7d098580ce4f · inbound

The Gaussian Minkowski problem for epigraphs of convex functions cites this paper.

The Gaussian Minkowski problem for epigraphs of convex functions A Minkowski problem for $\alpha$-concave functions via optimal transport

Reference 20

Resolution
verified exact
local_arxiv, observed 2026-08-15T17:28:49.889581Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=arxiv_source observed=2026-08-15T17:28:49.682827Z digest=sha256:87b54646176a8adc53c70b38f369657b5d22ebaae78d45954b6463b4f3457327