Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-10T21:34:43.920963Z
Paper Citation Record · LEDGER
As of 22 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 7 inbound Pith citation observations for arXiv:2501.04656.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-10T21:34:43.920963Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-15T16:56:26.221531Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-03T08:17:45.178501Z
39 of 39 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 61b65d37-9300-4c96-ad2c-503cbe856ba0 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Stability of the pr \'e kopa--leindler inequality
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 70c5970b-61fa-475a-a6f3-cae859ce2890 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities o r \"o czky. Stability of some versions of the Pr \'e kopa--Leindler inequality. Monatshefte f \
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 13580aa7-39a6-4116-a0e9-e0c33cd67410 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Stability of the Pr \'e kopa-Leindler inequality for log-concave functions
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation c2e870a8-91c5-4467-8984-b7da182430ff · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Lower bounds for the Pr \'e kopa-Leindler deficit by some distances modulo translations
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 2c8db365-0af3-4281-9fff-c6f5ffeb8852 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities A quantitative stability result for the Pr \'e kopa--Leindler inequality for arbitrary measurable functions
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 765a6a69-a1f9-4084-ba78-c57e9e73135c · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Robustness of the G aussian concentration inequality and the B runn- M inkowski inequality
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 39d8c5b2-d932-4145-a338-74ba86ad9192 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Balogh and Alexandru Kristály
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 4a403af4-360d-4aa9-aa1c-f09f984ff55e · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 6572df99-806a-4b68-bbe7-005ae2409788 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Unresolved cited work
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 14d7d0cb-727a-48a7-8c77-2bd98ccebe08 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Near Equality in the Brunn-Minkowski Inequality
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 6ad20cff-35f9-42d3-b174-97f993ec564a · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Near equality in the two-dimensional Brunn-Minkowski inequality
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation a040be11-aacc-4dc2-a59e-66d7fddc89c2 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Stability for the Brunn-Minkowski and Riesz rearrangement inequalities, with applications to G aussian concentration and finite range non-local isoperimetry
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 6ce1a41c-6d0f-4384-a2c7-589942eaf6c2 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Crit \`e res de convexit \'e et in \'e galit \'e s int \'e grales
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 002d9382-4bd5-4f1e-b859-8c9047fa3958 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Dimensionality and the stability of the Brunn--Minkowski inequality
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation fc35167c-117d-44c6-bbdf-71653cd764ae · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Stability results for the Brunn--Minkowski inequality
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 36372483-19a3-4617-92b5-3898c1f9b017 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Quantitative stability for sumsets in R ^n
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 30ca61a4-a6c0-4f33-9d3b-05a610d61530 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Quantitative stability for the Brunn--Minkowski inequality
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 0a7bdbf0-8b8e-4bc5-b617-3602b46745e7 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities A sharp Freiman type estimate for semisums in two and three dimensional Euclidean spaces
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 914a272a-0a16-44bf-b1a7-d0aed4bf6c5e · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities The sharp quantitative E uclidean concentration inequality
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 1e845cd6-a9b1-4bd2-9e29-c3f056f542a7 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities The sharp quantitative isoperimetric inequality
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation f1214e4a-9ec3-4949-a619-8dc478d2fea8 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities A refined B runn- M inkowski inequality for convex sets
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation b7f526c3-422d-487b-ae5f-d0c41ae730df · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities A mass transportation approach to quantitative isoperimetric inequalities
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation aa1be0c9-75c3-4f75-8d7b-195c76e3d4a0 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities A mass transportation approach to quantitative isoperimetric inequalities
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation a2ce1852-94c8-444b-905d-9811c27f8033 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Improved stability versions of the Pr\'ekopa-Leindler inequality
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 5c7d8d3f-7d2b-4151-9d06-585ae6166e67 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Sharp stability of the Brunn-Minkowski inequality via optimal mass transportation
Reference 26
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ef662626-6c4c-47c6-b845-5e847de934f9 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities The Brunn-Minkowski inequality
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 3324cac8-c7fb-4d26-bd9b-59a199ed3fec · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Quantitative Borell-Brascamp-Lieb inequalities for power concave functions
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 7d80ac2b-b509-4dbc-a85c-8fbbd503dcb5 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Locality in Sumsets
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 40c1ccf0-f186-46cf-a00f-312d170b394d · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities The sharp doubling threshold for approximate convexity
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 553b20f2-8b81-4caa-947a-3e8b1c77469f · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Sharp stability of Brunn--Minkowski for homothetic regions
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 3eb52643-1a3c-4a20-bfc3-e40813950d98 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Sharp L^1 I nequalities for S up- C onvolution
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation e8ba02a1-e5de-4a62-a5d3-e454e733936c · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Sharp quantitative stability of the planar Brunn--Minkowski inequality
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 347d7f2f-488e-46a6-b491-eaa92cd65035 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Ein beweis des fixpunktsatzes f \"u r n -dimensionale simplexe (in G erman)
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation f2a1a342-7f74-40bd-8149-9416df017275 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Stability for Borell-Brascamp-Lieb inequalities
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 1bc22f89-23c7-4a7b-8da5-e74ac26db303 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Diameter of sets and measure of sumsets
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation bc3802db-5c57-4bed-b4e8-dbebfc381353 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities The Brunn--Minkowski inequality and nonconvex sets
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 913901cc-e473-4e6d-9c73-f3af6cf798c9 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Additive combinatorics and geometry of numbers
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation a9273cbd-226d-4d5b-9c77-81c312ef680c · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Convex bodies: the Brunn--Minkowski theory , volume 151
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 4f5a4fdf-cdca-475c-ba90-d8889d2feed2 · outbound
Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities Sharp quantitative stability of the Brunn-Minkowski inequality
Reference 40
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5bcdcf06-be3d-4a8e-a3c3-34eccab9b544 · inbound
Equality in Liakopoulos's generalized dual Loomis-Whitney inequality via Barthe's Reverse Brascamp-Lieb inequality Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 3723153b-a842-43e6-b064-0fcafe5f5b67 · inbound
Sharp stability in hypercontractivity estimates and logarithmic Sobolev inequalities Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities
Reference 31
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ec031df7-e288-4074-b50b-aa068db2c4ab · inbound
Quantitative stability for the Brascamp-Lieb inequality and moment measures Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities
Reference 2024
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e6d1f648-34dd-4702-b7ed-829c76fb95e1 · inbound
On Ball's conjectured Santal\'o type inequality Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities
Reference 15
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9456c252-b603-4c27-920e-51d23ea8fb8b · inbound
The sharp threshold for Hausdorff convexification under Minkowski addition Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation d48142a1-83c0-43c2-a933-3871c5d1f7ae · inbound
Tight Stability Estimates Near the Simplex and Improved Bounds for the Diameter of the Banach-Mazur Compactum in Fixed Dimensions Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities
Reference 16
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b6db2c7c-7bda-422d-8294-cd1f9e8829f8 · inbound
Quantitative stability for Bakry--\'Emery log-Sobolev and Talagrand inequalities Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities
Reference 35
Source-reported events for the cited work
Unavailable: canonical work link unavailable.