Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T13:50:10.640949Z
Paper Citation Record · LEDGER
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form
As of 12 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 2 inbound Pith citation observations for arXiv:2412.12819.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-04T07:21:36.467293Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-07-08T06:44:40.206164Z
Reference resolution
46 of 46 outbound references displayed
- verified exact2
- verified fuzzy26
- unresolved18
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation b08f84f0-c885-4205-abcc-e0a58c052a64 · outbound
This paper cites Aubin, Equations diff\'erentielles non lin\'eaires et probl\`eme de Y amabe concernant la courbure scalaire , J.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Aubin, Equations diff\'erentielles non lin\'eaires et probl\`eme de Y amabe concernant la courbure scalaire , J
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:11.373074Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 7459a77e-6e7d-45b0-b83e-3f720811a418 · outbound
This paper cites Bianchi and H.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Bianchi and H
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:11.356861Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 5841be01-1a45-452d-8854-5d07b61c67be · outbound
This paper cites Bonforte, J.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Bonforte, J
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:11.341160Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 39f962ec-e57c-450a-9dd7-912c86b9de32 · outbound
This paper cites Stability in Gagliardo-Nirenberg-Sobolev inequalities: flows, regularity and the entropy method.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Stability in Gagliardo-Nirenberg-Sobolev inequalities: flows, regularity and the entropy method
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T13:50:10.444789Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cc97c3d4-99d6-48b6-9722-758cd7d4530d · outbound
This paper cites Brendle, Convergence of the Y amabe flow for arbitrary initial energy , J.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Brendle, Convergence of the Y amabe flow for arbitrary initial energy , J
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:11.325776Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation e0a0371e-4637-42ec-83a0-e4432c6fe3f5 · outbound
This paper cites Brendle, Convergence of the Y amabe flow in dimension 6 and higher , Invent.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Brendle, Convergence of the Y amabe flow in dimension 6 and higher , Invent
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:11.310221Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 7c10285b-4149-428c-b4ad-169be909b430 · outbound
This paper cites Brezis and E.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Brezis and E
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:11.295060Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 16cf839b-2b50-4294-8b59-4c26071312a3 · outbound
This paper cites Brigati, J.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Brigati, J
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:11.280287Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation eb6991e8-45d2-4cf4-ae16-364f127541ec · outbound
This paper cites Carlotto, O.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Carlotto, O
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:11.265426Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 6ba19b98-5474-4595-8de5-ebaddcecb48e · outbound
This paper cites an unresolved cited work.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T13:50:11.250016Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation ae3e2b20-cc39-45b6-affe-35031ea10633 · outbound
This paper cites an unresolved cited work.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T13:50:11.235021Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation ca494c33-f82b-40d7-943b-8ad3210ca175 · outbound
This paper cites Cianchi, N.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Cianchi, N
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:11.219673Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation fabfaa0c-d3b4-433b-930f-14be27c4a389 · outbound
This paper cites an unresolved cited work.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T13:50:11.204868Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation e8a6649f-f074-438b-9e0d-2c8ea4af3efa · outbound
This paper cites an unresolved cited work.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T13:50:11.190356Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation aa558ec1-7c5a-40e4-b937-d767f821fe6f · outbound
This paper cites an unresolved cited work.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T13:50:11.176004Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation f8fede8b-06ac-4694-945e-8e10f10cb899 · outbound
This paper cites Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence
Reference 16
- Resolution
- verified exact
- local_arxiv, observed 2026-08-11T13:50:10.707154Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 2fd8bebb-76cb-4c90-829f-83e37271362b · outbound
This paper cites Engelstein, R.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Engelstein, R
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:11.161586Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 9d0ba00d-6059-4a4b-9c1b-28a0748b9a40 · outbound
This paper cites Figalli and R.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Figalli and R
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:11.146568Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 54dd3eff-b487-4ca1-a23a-96ec137cfdc4 · outbound
This paper cites Figalli and Y.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Figalli and Y
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:11.131928Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation e63f87b6-8a48-42fc-b7d0-404863ab21b3 · outbound
This paper cites an unresolved cited work.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T13:50:11.117180Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 0bf1375d-ac08-4dfc-b8af-9b69699b433c · outbound
This paper cites an unresolved cited work.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T13:50:11.102545Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 6c0c68bf-75f0-476c-aae6-bd2b4dc730d4 · outbound
This paper cites an unresolved cited work.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T13:50:11.086585Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation d7c72a97-93c8-4efb-89ac-fd04137f2fa9 · outbound
This paper cites an unresolved cited work.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T13:50:11.071624Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 95c3baa2-65de-4d07-8b24-1701ed693423 · outbound
This paper cites an unresolved cited work.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T13:50:11.056703Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation b0f32ec3-2910-4f2d-b16a-f8e79196aec1 · outbound
This paper cites Ge and G.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Ge and G
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:11.041771Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 616ff6f6-4a71-443b-9831-1148c5df4155 · outbound
This paper cites Ge and G.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Ge and G
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:11.026719Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation c6637ad1-3e3b-4794-939a-dd551f145d9e · outbound
This paper cites an unresolved cited work.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T13:50:11.011872Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 5f761703-260d-4ab4-afae-675b96eecada · outbound
This paper cites Guan and G.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Guan and G
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:10.996068Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation a7c264dd-d7d1-48fb-b131-9df933829679 · outbound
This paper cites Sharp quantitative stability of the M\"obius group among sphere-valued maps in arbitrary dimension.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Sharp quantitative stability of the M\"obius group among sphere-valued maps in arbitrary dimension
Reference 29
- Resolution
- verified exact
- local_arxiv, observed 2026-08-11T13:50:10.684913Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 95d60598-0ca0-4f09-af2f-e4ec35232903 · outbound
This paper cites an unresolved cited work.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Unresolved cited work
Reference 30
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T13:50:10.981407Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation cc163ae0-f591-48d8-a3e1-b8e9ec5c575a · outbound
This paper cites K \"o nig, An exceptional property of the one-dimensional bianchi--egnell inequality, Calc.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form K \"o nig, An exceptional property of the one-dimensional bianchi--egnell inequality, Calc
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:10.967215Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation e3d31f17-82a8-4bdc-bbaa-148a83353a34 · outbound
This paper cites an unresolved cited work.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Unresolved cited work
Reference 32
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T13:50:10.952244Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 422be015-ed68-42a9-8cb9-77673761d4e9 · outbound
This paper cites Li and Y.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Li and Y
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:10.937907Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation ad479aa3-093b-4087-b9be-900691c5d865 · outbound
This paper cites Lions, The C oncentration- C ompactness P rinciple in the C alculus of V ariations.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Lions, The C oncentration- C ompactness P rinciple in the C alculus of V ariations
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:10.923181Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 2c59ecdc-21f4-4673-bb94-a07338e64ecf · outbound
This paper cites Lions, The C oncentration- C ompactness P rinciple in the C alculus of V ariations.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Lions, The C oncentration- C ompactness P rinciple in the C alculus of V ariations
Reference 35
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:10.907607Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 2cc7c7af-e9cf-4e05-b907-d0a68423ebb3 · outbound
This paper cites Neumayer, A note on strong-form stability for the S obolev inequality , Calc.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Neumayer, A note on strong-form stability for the S obolev inequality , Calc
Reference 36
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:10.893435Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 14df7af2-346a-41a6-a3e7-f8b01586fcb3 · outbound
This paper cites Obata, The conjectures on conformal transformations of R iemannian manifolds , J.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Obata, The conjectures on conformal transformations of R iemannian manifolds , J
Reference 37
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:10.878366Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 5f19473d-f675-4114-af9d-507145ee8946 · outbound
This paper cites Rodemich, The S obolev inequality with best possible constant , Analysis Seminar Caltech (1966).
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Rodemich, The S obolev inequality with best possible constant , Analysis Seminar Caltech (1966)
Reference 38
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:10.863316Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 6a304329-a1ac-4e4a-832e-42cb308a6759 · outbound
This paper cites an unresolved cited work.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Unresolved cited work
Reference 39
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T13:50:10.848040Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 1421c4cb-da37-4552-b6a5-e2de225223f2 · outbound
This paper cites Sheng, N.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Sheng, N
Reference 40
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:10.832358Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 8c3222de-151b-4fa6-a269-15cd6905ba5e · outbound
This paper cites Sheng, N.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Sheng, N
Reference 41
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:10.816829Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 011b4c58-3dc5-42d0-89c2-fd1084cb3fb5 · outbound
This paper cites an unresolved cited work.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Unresolved cited work
Reference 42
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T13:50:10.800495Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation ed18b315-c701-46bd-8d59-0089c2a5333a · outbound
This paper cites Talenti, B est constant in S obolev inequality , Ann.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Talenti, B est constant in S obolev inequality , Ann
Reference 43
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:10.785400Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 58aa1132-8571-4df4-a8e8-fed6436294f1 · outbound
This paper cites an unresolved cited work.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Unresolved cited work
Reference 44
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T13:50:10.770378Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 65055fa3-a3be-4207-bf6b-949892a6ec80 · outbound
This paper cites an unresolved cited work.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Unresolved cited work
Reference 45
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T13:50:10.754889Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation a82106c3-500e-4bc0-a146-a2506b9d3478 · outbound
This paper cites Yamabe, On a deformation of R iemannian structures on compact manifolds , Osaka Math.
The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form Yamabe, On a deformation of R iemannian structures on compact manifolds , Osaka Math
Reference 46
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T13:50:10.740020Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Pith citing papers
Observation c0a07fcd-3d27-468d-b536-ee81234734bc · inbound
Quantitative Lorentzian isoperimetric inequalities in conical Minkowski spacetimes cites this paper.
Quantitative Lorentzian isoperimetric inequalities in conical Minkowski spacetimes The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form
Reference 35
- Resolution
- unresolved
- no resolver link, observed 2026-08-04T07:21:36.467293Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 64aecc40-c38f-47b1-af12-56b9f8ee0aa0 · inbound
Stability for the Affine Sobolev Inequality and its Critical Points for $p\ge 2$ cites this paper.
Stability for the Affine Sobolev Inequality and its Critical Points for $p\ge 2$ The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form
Reference 26
- Resolution
- verified exact
- local_arxiv, observed 2026-07-08T06:44:40.208078Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.