Paper Citation Record · LEDGER

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group

As of 24 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2509.08415.

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

pith.paper-citation-record.v1
2509.08415 v1

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T20:56:23.914306Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+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

34 of 34 outbound references displayed

verified exact1
verified fuzzy27
unresolved6
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0cd26a1d-3ada-4ee7-9890-f3a680ffbf81 · outbound

This paper cites Birindelli, I.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Birindelli, I

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.393573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation edc78db0-5a59-4324-96df-18f4142e2d64 · outbound

This paper cites Caffarelli, L.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Caffarelli, L

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.380992Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation ae039150-8f2e-4770-8d00-835e100c9305 · outbound

This paper cites Caffarelli, Basilis Gidas, and Joel Spruck.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Caffarelli, Basilis Gidas, and Joel Spruck

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.369521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 063318fa-80d2-44a7-8a0a-2a01ae3eed5d · outbound

This paper cites A Liouville theorem in the Heisenberg group.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group A Liouville theorem in the Heisenberg group

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-04T20:56:23.805601Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7dccdfde-2a54-47b9-9960-7b6849617768 · outbound

This paper cites Monticelli, and Alberto Roncoroni.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Monticelli, and Alberto Roncoroni

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.356480Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 28c16b36-61a7-409c-bd18-ffc39c98cf3e · outbound

This paper cites Chang, Matthew J.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Chang, Matthew J

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.344068Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 6e31342f-9eaf-47af-9cf9-5321be2652a3 · outbound

This paper cites Classification of solutions of some nonlinear elliptic equations.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Classification of solutions of some nonlinear elliptic equations

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.318842Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 12300bc0-cbfa-47fa-8e79-5c76eca8b117 · outbound

This paper cites Symmetry results for critical anisotropicp- Laplacian equations in convex cones.Geom.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Symmetry results for critical anisotropicp- Laplacian equations in convex cones.Geom

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.306734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 19d9523c-f63d-4ba3-a6a9-a07046808042 · outbound

This paper cites Notions of convexity in Carnot groups.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Notions of convexity in Carnot groups

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.293443Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation acd00b9e-f25e-4e75-808b-7cfd46f5b8aa · outbound

This paper cites Liouville-type results for the CR Yamabe equation in the Heisenberg group.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Liouville-type results for the CR Yamabe equation in the Heisenberg group

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T20:56:23.832294Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1993c329-eb32-44eb-9055-2e298f53a038 · outbound

This paper cites On the solvability for a p-k-Hessian inequality.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group On the solvability for a p-k-Hessian inequality

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-08-04T20:56:23.952624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation eaa42b94-20ed-407f-a0f3-a388f656e35a · outbound

This paper cites Gidas and J.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Gidas and J

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.280354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 9010f932-1180-4c3c-958b-bd45825e74fb · outbound

This paper cites an unresolved cited work.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-04T20:56:24.267223Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 9f11c9d8-3eab-4a15-bcfe-106d1f90eda5 · outbound

This paper cites an unresolved cited work.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-04T20:56:24.253946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f6f1b52a-4820-41b3-ab89-65ec6b688ca5 · outbound

This paper cites an unresolved cited work.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-04T20:56:24.240783Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 2c0d093f-4d26-4773-bdf6-98497c96a7ab · outbound

This paper cites Manfredi, and Bianca Stroffolini.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Manfredi, and Bianca Stroffolini

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.227273Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 2f5e65e5-f358-47d4-b4de-a4be7aafeea1 · outbound

This paper cites A Liouville theorem for a class semilinear elliptic equations on the Heisenberg group.Adv.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group A Liouville theorem for a class semilinear elliptic equations on the Heisenberg group.Adv

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.214025Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 68ffe75d-1bdb-4af6-ad22-a7076cdada93 · outbound

This paper cites The conjectures on conformal transformations of Riemannian manifolds.J.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group The conjectures on conformal transformations of Riemannian manifolds.J

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.200450Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 25d4a3a2-8357-43b1-bd0c-24568b8b9916 · outbound

This paper cites Nonexistence results for Hessian inequality.Methods Appl.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Nonexistence results for Hessian inequality.Methods Appl

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.187427Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation bef61643-3a47-40a1-8f7f-0c7f2a77ddfd · outbound

This paper cites Singularities and Liouville theorems for some special conformal Hessian equations.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Singularities and Liouville theorems for some special conformal Hessian equations

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.173747Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f8f63340-e8a1-41d5-98ed-ca4186d7d20c · outbound

This paper cites On the classification of entire solutions to the critical p-Laplace equation.Math.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group On the classification of entire solutions to the critical p-Laplace equation.Math

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.158795Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 875df032-181f-4eaf-98bf-4315a5f94bb2 · outbound

This paper cites Verbitsky.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Verbitsky

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.144471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 5a7d4b94-9ca7-45a3-a1f9-affacc621299 · outbound

This paper cites Verbitsky.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Verbitsky

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.130315Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 198f75a8-f305-4cf2-9f48-8ab216b76741 · outbound

This paper cites Classification of positiveD 1,p(RN )-solutions to the criticalp-Laplace equation in RN .Adv.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Classification of positiveD 1,p(RN )-solutions to the criticalp-Laplace equation in RN .Adv

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.116945Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation bc57bb07-0927-434f-b0fa-b8177172e2f0 · outbound

This paper cites Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities.Acta Math., 189(1):79–142, 2002.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities.Acta Math., 189(1):79–142, 2002

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.103546Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 373470e6-ced1-4e47-bb22-b3c69e7f34ba · outbound

This paper cites Stein.Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, volume 43 ofPrinceton Mathematical Series.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Stein.Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, volume 43 ofPrinceton Mathematical Series

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-04T20:56:23.889886Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6d236826-9f5b-49ce-b6e7-936e99bde24a · outbound

This paper cites Trudinger and Xu-Jia Wang.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Trudinger and Xu-Jia Wang

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.080079Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a84c39f8-9ed7-471f-afd6-a4913cf91150 · outbound

This paper cites Trudinger and Xu-Jia Wang.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Trudinger and Xu-Jia Wang

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.066144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 77d89ac2-8b00-425a-bad1-2ac5be9712e9 · outbound

This paper cites Trudinger and Xu-Jia Wang.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Trudinger and Xu-Jia Wang

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.051359Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 93eb2dbf-03c0-4073-90b9-5a7b1ca8b1dd · outbound

This paper cites Trudinger and Wei Zhang.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Trudinger and Wei Zhang

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.037761Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation d96c828e-f9ad-46ac-abe2-02ec037cce83 · outbound

This paper cites A priori estimates and application to the symmetry of solutions for criticalp-Laplace equations.J.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group A priori estimates and application to the symmetry of solutions for criticalp-Laplace equations.J

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.024465Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 28864d6a-1060-4ee8-939f-11e21e37a41b · outbound

This paper cites A Liouville theorem for superlinear parabolic equations on the Heisenberg group.Adv.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group A Liouville theorem for superlinear parabolic equations on the Heisenberg group.Adv

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.010547Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 32400c42-0bcd-42a5-8175-c3afc3e777ad · outbound

This paper cites Semi-linear Liouville theorems in the Heisenberg group via vector field methods.J.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Semi-linear Liouville theorems in the Heisenberg group via vector field methods.J

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:23.996582Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a12eaf8e-f2b2-4f4c-9ebb-6da807d4f7c5 · outbound

This paper cites Press, Somerville, MA, 2003.

A Liouville theorem for the $2$-Hessian equation on the Heisenberg group Press, Somerville, MA, 2003

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:56:24.331034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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