Paper Citation Record · LEDGER

Rigidity for perimeter inequality under spherical symmetrisation

As of 22 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:1908.04865.

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

pith.paper-citation-record.v1
1908.04865 v2

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T13:36:02.032514Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

32 of 32 outbound references displayed

verified exact0
verified fuzzy23
unresolved9
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7f884161-aa45-4d1b-ac3f-8f417ef729ae · outbound

This paper cites Ambrosio, V.

Rigidity for perimeter inequality under spherical symmetrisation Ambrosio, V

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.498985Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 013ac339-a001-4599-9856-12ef5e1e172e · outbound

This paper cites Ambrosio, N.

Rigidity for perimeter inequality under spherical symmetrisation Ambrosio, N

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.484479Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 1ba17ab2-27fd-449d-9972-a2b1185ef20e · outbound

This paper cites Barchiesi, F.

Rigidity for perimeter inequality under spherical symmetrisation Barchiesi, F

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.470368Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6ecfa3ef-3f5d-493f-ad0e-1006e919ba0f · outbound

This paper cites Bartsch, T.

Rigidity for perimeter inequality under spherical symmetrisation Bartsch, T

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.457239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation cd34e906-bd66-461a-981d-a4414471422f · outbound

This paper cites Baernstein, A uniﬁed approach to symmetrization , Symposia Matematica, 35 (1995), pp.

Rigidity for perimeter inequality under spherical symmetrisation Baernstein, A uniﬁed approach to symmetrization , Symposia Matematica, 35 (1995), pp

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.443148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e6936fda-f860-4f29-8fa3-d7442d8acc42 · outbound

This paper cites an unresolved cited work.

Rigidity for perimeter inequality under spherical symmetrisation Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:36:02.429679Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 36c27424-d17a-413f-ac95-502b4276e5dc · outbound

This paper cites B ¨ogelein, F.

Rigidity for perimeter inequality under spherical symmetrisation B ¨ogelein, F

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.415189Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f058af19-fec0-43e3-93c2-da89ac556971 · outbound

This paper cites an unresolved cited work.

Rigidity for perimeter inequality under spherical symmetrisation Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-14T13:36:01.907165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ba8dcf6b-a9c9-4243-88cf-9eac16e68475 · outbound

This paper cites Cagnetti, M.

Rigidity for perimeter inequality under spherical symmetrisation Cagnetti, M

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.394045Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c89d3d3c-ab86-4704-9c93-704f09308615 · outbound

This paper cites an unresolved cited work.

Rigidity for perimeter inequality under spherical symmetrisation Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-14T13:36:01.915594Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9ee32239-5e4a-4ef3-90ff-642f2d60a718 · outbound

This paper cites an unresolved cited work.

Rigidity for perimeter inequality under spherical symmetrisation Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:36:02.371660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 96142a1d-615c-4d4c-9cc0-ba72a86ad0c7 · outbound

This paper cites Chleb´ık, A.

Rigidity for perimeter inequality under spherical symmetrisation Chleb´ık, A

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.354382Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 25d20160-1a5f-4df2-b9b7-4f1027a83531 · outbound

This paper cites Cianchi and N.

Rigidity for perimeter inequality under spherical symmetrisation Cianchi and N

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.342126Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3527a0bf-43cd-4bbc-b20d-9ce7c56f1e0b · outbound

This paper cites Math., 203 (2006), pp.

Rigidity for perimeter inequality under spherical symmetrisation Math., 203 (2006), pp

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.328574Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 1048640b-5575-43ab-bcec-ec77d4031a48 · outbound

This paper cites Cianchi, N.

Rigidity for perimeter inequality under spherical symmetrisation Cianchi, N

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.312703Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 086f2e34-b59b-4d64-84c4-1afedaf67a8c · outbound

This paper cites De Giorgi, Sulla propriet` a isoperimetrica dell’ipersfera, nella classe degli insiemi aventi frontiera orientata di misura ﬁnita , Atti Accad.

Rigidity for perimeter inequality under spherical symmetrisation De Giorgi, Sulla propriet` a isoperimetrica dell’ipersfera, nella classe degli insiemi aventi frontiera orientata di misura ﬁnita , Atti Accad

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.299438Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 28ce454d-82b7-4887-8bed-1fd50f3f8c38 · outbound

This paper cites [Author name on title page: Ennio Giorgi], Edited by Luigi Ambrosio, Gianni Dal Maso, Marco Forti, Mario Miranda and Sergio Spagnolo, Reprint of the 2006 edition.

Rigidity for perimeter inequality under spherical symmetrisation [Author name on title page: Ennio Giorgi], Edited by Luigi Ambrosio, Gianni Dal Maso, Marco Forti, Mario Miranda and Sergio Spagnolo, Reprint of the 2006 edition

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-14T13:36:01.946069Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d6d36c25-8bc5-4064-9693-816ca9a8a6b3 · outbound

This paper cites Giaquinta, G.

Rigidity for perimeter inequality under spherical symmetrisation Giaquinta, G

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-14T13:36:01.950406Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0010859b-6243-41fb-86d6-881bf3a3581c · outbound

This paper cites Gidas, W.M.

Rigidity for perimeter inequality under spherical symmetrisation Gidas, W.M

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.270853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3519c7c1-bf53-4190-9cc0-c353ee19e20e · outbound

This paper cites Kawohl, Rearrangements and convexity of level sets in PDE , vol.

Rigidity for perimeter inequality under spherical symmetrisation Kawohl, Rearrangements and convexity of level sets in PDE , vol

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.258811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f2f7b6cc-8bc6-4a85-9c1c-a016b068c7b7 · outbound

This paper cites Rational Mech.

Rigidity for perimeter inequality under spherical symmetrisation Rational Mech

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.246377Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a7187339-1d98-4342-aa68-2a93f770256f · outbound

This paper cites Maggi, Sets of ﬁnite perimeter and geometric variational problems, vol.

Rigidity for perimeter inequality under spherical symmetrisation Maggi, Sets of ﬁnite perimeter and geometric variational problems, vol

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.233474Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3a3c98a0-46e0-4674-b1fc-8ae76046c763 · outbound

This paper cites McGillivray, An isoperimetric inequality in the plane with a log-convex density , Ric.

Rigidity for perimeter inequality under spherical symmetrisation McGillivray, An isoperimetric inequality in the plane with a log-convex density , Ric

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.217614Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 776b03e7-72a5-418d-b9f4-b7235839de48 · outbound

This paper cites Morgan, S.

Rigidity for perimeter inequality under spherical symmetrisation Morgan, S

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.200988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0c6b25ec-3c80-4608-a135-06601d5436e8 · outbound

This paper cites Morgan, A.

Rigidity for perimeter inequality under spherical symmetrisation Morgan, A

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.187174Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4ad175ae-0d5c-4e85-8065-bc4670427589 · outbound

This paper cites Perugini, Rigidity of Steiner’s inequality for the anisotropic perimeter (preprint).

Rigidity for perimeter inequality under spherical symmetrisation Perugini, Rigidity of Steiner’s inequality for the anisotropic perimeter (preprint)

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.173832Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation afefdefc-6d00-4e0c-adc5-bd75e70d48cd · outbound

This paper cites P´olya, Sur la sym´ etrisation circulaire.

Rigidity for perimeter inequality under spherical symmetrisation P´olya, Sur la sym´ etrisation circulaire

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.160661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 462ed7b5-08e1-4132-8c11-4ce1df284d7e · outbound

This paper cites an unresolved cited work.

Rigidity for perimeter inequality under spherical symmetrisation Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:36:02.145528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6af1c1ae-092a-4e84-be46-4eb1898e2ed9 · outbound

This paper cites Serrin, A symmetry property in potential theory , Arch.

Rigidity for perimeter inequality under spherical symmetrisation Serrin, A symmetry property in potential theory , Arch

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.130496Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d15e95fa-8a9e-4911-8ea2-114c8f1f83ad · outbound

This paper cites an unresolved cited work.

Rigidity for perimeter inequality under spherical symmetrisation Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:36:02.110440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b299b4ba-028f-42ef-b71f-cf72f1e03d1a · outbound

This paper cites Smets, M.

Rigidity for perimeter inequality under spherical symmetrisation Smets, M

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:36:02.093281Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 435105d0-4005-4a3e-9943-5b94880d7253 · outbound

This paper cites an unresolved cited work.

Rigidity for perimeter inequality under spherical symmetrisation Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-14T13:36:02.075819Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Pith citing papers

No inbound Pith citation observations are available.