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Paper Citation Record · LEDGER

Free energy minimizers with radial densities: classification and quantitative stability

As of 13 August 2026, this Paper Citation Record lists 69 of 69 outbound references and 1 inbound Pith citation observation for arXiv:2412.03997.

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measured 69 of 69 reference resolution

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Pith citing papers itemized under the disclosed page cap.

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Reference resolution

69 of 69 outbound references displayed

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Outbound references

Observation dbc9e99f-9816-4e41-8cba-b2b3032802fb · outbound

This paper cites Ambrosio, N.

Free energy minimizers with radial densities: classification and quantitative stability Ambrosio, N

Reference 1

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Observation 60e85712-f053-4180-91c4-6d2ea3c938fe · outbound

This paper cites New spectral Bishop-Gromov and Bonnet-Myers theorems and applications to isoperimetry.

Free energy minimizers with radial densities: classification and quantitative stability New spectral Bishop-Gromov and Bonnet-Myers theorems and applications to isoperimetry

Reference 2

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Observation c657a0d2-c848-4cb2-99b9-3e1dd5bbe405 · outbound

This paper cites Equilibrium shapes of cr ystals in a gravitational field: Crystals on a table.

Free energy minimizers with radial densities: classification and quantitative stability Equilibrium shapes of cr ystals in a gravitational field: Crystals on a table

Reference 3

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This paper cites Diffusions hypercontractives.

Free energy minimizers with radial densities: classification and quantitative stability Diffusions hypercontractives

Reference 4

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Observation 8d77b5d1-b138-478c-aaea-9b4fb746c4bd · outbound

This paper cites Lévy–Gromov’s isoperimetric in equality for an infinite di- mensional diffusion generator.

Free energy minimizers with radial densities: classification and quantitative stability Lévy–Gromov’s isoperimetric in equality for an infinite di- mensional diffusion generator

Reference 5

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This paper cites Stability of hypersurface s with constant mean curvature.

Free energy minimizers with radial densities: classification and quantitative stability Stability of hypersurface s with constant mean curvature

Reference 6

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Observation 943d0311-c87b-4908-a2c5-96158adfa4fa · outbound

This paper cites Propriétés de concavité du profil isopérimétr ique et applications.

Free energy minimizers with radial densities: classification and quantitative stability Propriétés de concavité du profil isopérimétr ique et applications

Reference 7

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Observation f466f649-6cb8-422a-be28-c9884363b2a7 · outbound

This paper cites A quantitative iso perimetric inequality on the sphere.

Free energy minimizers with radial densities: classification and quantitative stability A quantitative iso perimetric inequality on the sphere

Reference 8

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This paper cites A sharp quantita tive isoperimetric in- equality in hyperbolic n-space.

Free energy minimizers with radial densities: classification and quantitative stability A sharp quantita tive isoperimetric in- equality in hyperbolic n-space

Reference 9

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This paper cites Isoperimetry in sur- faces of revolution with density.

Free energy minimizers with radial densities: classification and quantitative stability Isoperimetry in sur- faces of revolution with density

Reference 10

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Observation fc4ace88-e264-48b0-9de6-378e78d03b4d · outbound

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Free energy minimizers with radial densities: classification and quantitative stability Isoperimetric Regions in Rn with Density rp

Reference 11

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Free energy minimizers with radial densities: classification and quantitative stability Unresolved cited work

Reference 12

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This paper cites Stabilité isopérimétrique.

Free energy minimizers with radial densities: classification and quantitative stability Stabilité isopérimétrique

Reference 13

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Free energy minimizers with radial densities: classification and quantitative stability Free boundary stable hypersu rfaces in manifolds with density and rigidity results

Reference 14

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Free energy minimizers with radial densities: classification and quantitative stability Proof of the log-convex density conjec ture

Reference 15

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Observation 73566fbc-d3b0-4c91-b6cb-4108c5264712 · outbound

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Free energy minimizers with radial densities: classification and quantitative stability The Riemann ian quantitative isoperi- metric inequality

Reference 16

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Free energy minimizers with radial densities: classification and quantitative stability On the i soperimetric deficit in Gauss space

Reference 17

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Free energy minimizers with radial densities: classification and quantitative stability A selection principle f or the sharp quantitative isoperimetric inequality

Reference 18

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Free energy minimizers with radial densities: classification and quantitative stability Best constants for the i soperimetric inequality in quantitative form

Reference 19

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Free energy minimizers with radial densities: classification and quantitative stability Sharp quantitative stability for isoperimetric inequalities with homogeneou s weights

Reference 20

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Free energy minimizers with radial densities: classification and quantitative stability Differential geometry of manifolds with den sity

Reference 21

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Free energy minimizers with radial densities: classification and quantitative stability A two-point function ap proach to connectedness of drops in convex potentials

Reference 22

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Free energy minimizers with radial densities: classification and quantitative stability A quantitativ e version of the isoperimetric inequality: the anisotropic case

Reference 23

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Free energy minimizers with radial densities: classification and quantitative stability A sharp stability result for t he relative isoperimetric inequality inside convex cones

Reference 24

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Free energy minimizers with radial densities: classification and quantitative stability On the isoperimetric problem f or radial log-convex den- sities

Reference 25

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Free energy minimizers with radial densities: classification and quantitative stability On the shape of liquid drops and crystals in the small mass regime

Reference 26

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Free energy minimizers with radial densities: classification and quantitative stability A mass transport ation approach to quantita- tive isoperimetric inequalities

Reference 27

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Free energy minimizers with radial densities: classification and quantitative stability Unresolved cited work

Reference 28

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Free energy minimizers with radial densities: classification and quantitative stability The sessile liquid drop. I. Symmetric case

Reference 29

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Free energy minimizers with radial densities: classification and quantitative stability Stability in the isoperimetric problem fo r convex or nearly spherical do- mains in Rn

Reference 30

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Free energy minimizers with radial densities: classification and quantitative stability The quantitative isoperimetric inequality and related topics

Reference 31

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Free energy minimizers with radial densities: classification and quantitative stability A strong form of the quantitative isoperimetric inequality

Reference 32

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Observation c22bd5cb-cfe1-408a-a41f-7823137d8edf · outbound

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Free energy minimizers with radial densities: classification and quantitative stability Some weighted isoperimetri c inequalities in quan- titative form

Reference 33

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Source-reported events for the cited work

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Observation a8a34fa5-0094-484b-80ca-2aeb7a98b5f9 · outbound

This paper cites The sharp quantita tive isoperimetric inequal- ity.

Free energy minimizers with radial densities: classification and quantitative stability The sharp quantita tive isoperimetric inequal- ity

Reference 34

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Observation e756b663-c90b-4de8-9203-2e096fbea40f · outbound

This paper cites Existence and regularity for the problem of a pendent liquid drop.

Free energy minimizers with radial densities: classification and quantitative stability Existence and regularity for the problem of a pendent liquid drop

Reference 35

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Observation 4dba083b-e7bf-4821-81a4-c8c99217dcae · outbound

This paper cites Isoperimetric inequalities in Riemannian manifolds.

Free energy minimizers with radial densities: classification and quantitative stability Isoperimetric inequalities in Riemannian manifolds

Reference 36

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source=pdf_text observed=2026-08-11T22:02:07.895115Z digest=sha256:c4d6e4bb16110f063f716e69a3c5f84fa742729db013549fd1ea0606f8ab85df

Observation 91af780a-ad3a-4cd9-95d4-6cb5fff4b5ef · outbound

This paper cites A quantitative isoperimetric inequality in n -dimensional space.

Free energy minimizers with radial densities: classification and quantitative stability A quantitative isoperimetric inequality in n -dimensional space

Reference 37

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Observation f565d358-787c-40c6-b65b-ff8c46511343 · outbound

This paper cites Some theorems on the free energies of cryst al surfaces.

Free energy minimizers with radial densities: classification and quantitative stability Some theorems on the free energies of cryst al surfaces

Reference 38

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Observation 3f32e8b3-c8ac-46e6-aa4b-673501b67891 · outbound

This paper cites The log-convex density conjecture and vertic al surface area in warped products.

Free energy minimizers with radial densities: classification and quantitative stability The log-convex density conjecture and vertic al surface area in warped products

Reference 39

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Observation 4768f7c4-820b-4cd4-b1e6-465b508078da · outbound

This paper cites A weighted relative isoperimetric inequal ity in convex cones.

Free energy minimizers with radial densities: classification and quantitative stability A weighted relative isoperimetric inequal ity in convex cones

Reference 40

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Observation e6e0ce60-7205-4ca0-bad6-c1aebc50cfdb · outbound

This paper cites On the equilibrium shape of a crystal.

Free energy minimizers with radial densities: classification and quantitative stability On the equilibrium shape of a crystal

Reference 41

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source=pdf_text observed=2026-08-11T22:02:07.940464Z digest=sha256:d4331def9c4e1a2757a6a51d136d601a1825be0ed6aeebd26c99ae0099374802

Observation e6ba1a55-265c-43af-8d5b-e3e680049019 · outbound

This paper cites The one-dimensional equilibrium shape of a crystal.

Free energy minimizers with radial densities: classification and quantitative stability The one-dimensional equilibrium shape of a crystal

Reference 42

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This paper cites Minimizing the free energy.

Free energy minimizers with radial densities: classification and quantitative stability Minimizing the free energy

Reference 43

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Observation dc20bf18-97ad-4054-91f9-3512c373f984 · outbound

This paper cites On the isoperimetric nature of a rearrangem ent inequality and its consequences for some variational problems.

Free energy minimizers with radial densities: classification and quantitative stability On the isoperimetric nature of a rearrangem ent inequality and its consequences for some variational problems

Reference 44

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source=pdf_text observed=2026-08-11T22:02:07.967150Z digest=sha256:8dc94fc0b134701a5e064452a3df3857403d4ab69caa1810835c3984eb581a79

Observation 20499b43-e599-48e7-93ae-f72c9fe51eb5 · outbound

This paper cites On isoperimetric se ts of radially symmetric measures.

Free energy minimizers with radial densities: classification and quantitative stability On isoperimetric se ts of radially symmetric measures

Reference 45

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source=pdf_text observed=2026-08-11T22:02:07.978057Z digest=sha256:a87ab7452a5c5a0894df6104ad2c40fa515539135fdc9978ae7c9d3868233991

Observation c38886d0-d211-487e-9b82-d2ef0dbf77a5 · outbound

This paper cites A class of weighted isoperimetric inequ alities in hyperbolic space.

Free energy minimizers with radial densities: classification and quantitative stability A class of weighted isoperimetric inequ alities in hyperbolic space

Reference 46

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source=pdf_text observed=2026-08-11T22:02:07.984915Z digest=sha256:72d4dbef4d282c77a14411f9e43018cd78386022a573ff7c9b63578965991db0

Observation dbbf492b-5824-4a34-800c-939ad2833853 · outbound

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Free energy minimizers with radial densities: classification and quantitative stability Unresolved cited work

Reference 47

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source=pdf_text observed=2026-08-11T22:02:07.991077Z digest=sha256:1af1ce35892c1faa41105eda1de59ccde2f8aa1a04765c11eaf3c4b6f8e89468

Observation 9af523e7-6add-4c4d-9fd1-88bb573622d5 · outbound

This paper cites an unresolved cited work.

Free energy minimizers with radial densities: classification and quantitative stability Unresolved cited work

Reference 48

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source=pdf_text observed=2026-08-11T22:02:07.998203Z digest=sha256:4ac7531ef9b0c6a80eaca471079bbc1a8da3ab40d327a282b90ed486bec22333

Observation bc2e25e7-50d9-4b1a-87b2-27561f52c710 · outbound

This paper cites Stable minimal hypersurfaces in $\mathbb R^6$.

Free energy minimizers with radial densities: classification and quantitative stability Stable minimal hypersurfaces in $\mathbb R^6$

Reference 49

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source=pdf_text observed=2026-08-11T22:02:08.007552Z digest=sha256:3ca61f05dc55f618b695e2295a0c87a7a7afaf6f0b7f5d6b6cf3d1521668fbc8

Observation 27e80527-8754-4b8f-b435-b7385e81394f · outbound

This paper cites Equilibrium shapes for planar crystals i n an external field.

Free energy minimizers with radial densities: classification and quantitative stability Equilibrium shapes for planar crystals i n an external field

Reference 50

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source=pdf_text observed=2026-08-11T22:02:08.016945Z digest=sha256:eecf292e6cdd0e3841805a34c508c86206dd5ec55ab4f9bd78544e494cba0228

Observation 477eea70-8163-479d-88cb-22384add76b8 · outbound

This paper cites A weighted isoperimetric inequality on the hyperbolic plane.

Free energy minimizers with radial densities: classification and quantitative stability A weighted isoperimetric inequality on the hyperbolic plane

Reference 51

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source=pdf_text observed=2026-08-11T22:02:08.023982Z digest=sha256:a9b79c83f81b894c52f6de5a91a0f7fe3a3399f907c523fce6fcc7aa2ed3701c

Observation 8a093251-9f3b-4892-85f3-bb6195288c0b · outbound

This paper cites An isoperimetric inequality in the pl ane with a log-convex density.

Free energy minimizers with radial densities: classification and quantitative stability An isoperimetric inequality in the pl ane with a log-convex density

Reference 52

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source=pdf_text observed=2026-08-11T22:02:08.032228Z digest=sha256:b1a54a50958f3c1ac69ad21009866fbde04238e9a216d3dfd82e615aa4b2c455

Observation d141401e-8f47-4a38-839f-9a3e8492d8bc · outbound

This paper cites an unresolved cited work.

Free energy minimizers with radial densities: classification and quantitative stability Unresolved cited work

Reference 53

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Observation 70c5c413-05ea-4192-9ff4-30ea8572879f · outbound

This paper cites Manifolds with density.

Free energy minimizers with radial densities: classification and quantitative stability Manifolds with density

Reference 54

Resolution
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source=pdf_text observed=2026-08-11T22:02:08.064659Z digest=sha256:70dcce6ca7644a9d32dddbcb7f2eb2ed2010e18b3ee227b24eee5f636a0b2cd1

Observation 49424e0f-1cb9-4243-bf75-d5b666dda01a · outbound

This paper cites Regularity of isoperimetric hypersurface s in Riemannian manifolds.

Free energy minimizers with radial densities: classification and quantitative stability Regularity of isoperimetric hypersurface s in Riemannian manifolds

Reference 55

Resolution
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source=pdf_text observed=2026-08-11T22:02:08.070060Z digest=sha256:a97bda6dc792c886fd0c9f794fc37465e360af6d2094ce1205c441c13d4ca6ff

Observation d549179e-01a7-4a28-9f1b-8623ac131797 · outbound

This paper cites Steiner and Schwarz s ymmetrization in warped products and fiber bundles with density.

Free energy minimizers with radial densities: classification and quantitative stability Steiner and Schwarz s ymmetrization in warped products and fiber bundles with density

Reference 56

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source=pdf_text observed=2026-08-11T22:02:08.078900Z digest=sha256:e5c4f45bd6c8d3546d1dfc147176ea77439cf93ed7033b0415f04f10140af078

Observation 2787dab5-3d93-40a1-bc33-40cf5b5457c5 · outbound

This paper cites Existence of isoperimetric regions in Rn with density.

Free energy minimizers with radial densities: classification and quantitative stability Existence of isoperimetric regions in Rn with density

Reference 57

Resolution
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source=pdf_text observed=2026-08-11T22:02:08.084724Z digest=sha256:d4a2c79991bf2390348821ce4e6f2ce05acb1ae8731ff8cf5b03b646aaa2c4d3

Observation 1c26f0de-3924-40a7-838f-987863d4b883 · outbound

This paper cites A strong form of the quantitative Wulff ine quality.

Free energy minimizers with radial densities: classification and quantitative stability A strong form of the quantitative Wulff ine quality

Reference 58

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source=pdf_text observed=2026-08-11T22:02:08.091828Z digest=sha256:c5e30266861498ee3323876b4b20370ce556b80751b14c65908c8565a9353fff

Observation a021dfbf-ed79-448a-a00e-86511bfad07f · outbound

This paper cites Stability of the Wulff shape.

Free energy minimizers with radial densities: classification and quantitative stability Stability of the Wulff shape

Reference 59

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source=pdf_text observed=2026-08-11T22:02:08.102813Z digest=sha256:e860a98a56b3a36e53d9263903a49cb3f58373a09687c422bd750afcfd9f7ece

Observation d24a13ac-a6cb-4a77-9a67-261c700e823d · outbound

This paper cites Regularity of free bounda ries in anisotropic capillar- ity problems and the validity of Young’s law.

Free energy minimizers with radial densities: classification and quantitative stability Regularity of free bounda ries in anisotropic capillar- ity problems and the validity of Young’s law

Reference 60

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source=pdf_text observed=2026-08-11T22:02:08.122084Z digest=sha256:784fc43a892976bd323e2189a2d7e7a329ea7377dec4e6faa5bc205615b93168

Observation e1a6e46d-27cc-4c3c-9ece-a3a7f306adb2 · outbound

This paper cites Stable and isoperimetric regions in some w eighted manifolds with boundary.

Free energy minimizers with radial densities: classification and quantitative stability Stable and isoperimetric regions in some w eighted manifolds with boundary

Reference 61

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source=pdf_text observed=2026-08-11T22:02:08.152836Z digest=sha256:c8805f604371aa1054f0ce9fc2084b0e9123050958d1fcddd456c5316eca2968

Observation 8052b423-7e77-4561-b939-88da01dffab3 · outbound

This paper cites On the is operimetric problem in Euclidean space with density.

Free energy minimizers with radial densities: classification and quantitative stability On the is operimetric problem in Euclidean space with density

Reference 62

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source=pdf_text observed=2026-08-11T22:02:08.159329Z digest=sha256:dcc5604cd2899b7f0c3f4c6f3a2b86826892101ad4ff9bde91b4f5efad8f5a70

Observation b2f29eda-b8d4-462b-af19-0b554e73dc3a · outbound

This paper cites Locally constrained inverse cur vature flows.

Free energy minimizers with radial densities: classification and quantitative stability Locally constrained inverse cur vature flows

Reference 63

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source=pdf_text observed=2026-08-11T22:02:08.166866Z digest=sha256:f47f3fc56340c034e33c430ea7bc3b65be8ddd49d3ebc0e9da8c0d48360a92c9

Observation 326d9e78-9089-4ab1-85cf-f75a06f976d7 · outbound

This paper cites Approaching the isoperimetric problem in H C m via the hyperbolic log- convex density conjecture.

Free energy minimizers with radial densities: classification and quantitative stability Approaching the isoperimetric problem in H C m via the hyperbolic log- convex density conjecture

Reference 64

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source=pdf_text observed=2026-08-11T22:02:08.175195Z digest=sha256:2397f4f27c5cb37cec6f739d080e21f3085997bf3683aa908b6f80d432c5b6bc

Observation 91e97efd-86e6-488d-bd44-a6ff63121b67 · outbound

This paper cites Quantitative C 1-stability of spheres in ra nk one symmetric spaces of non-compact type.

Free energy minimizers with radial densities: classification and quantitative stability Quantitative C 1-stability of spheres in ra nk one symmetric spaces of non-compact type

Reference 65

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source=pdf_text observed=2026-08-11T22:02:08.183585Z digest=sha256:fc9ec65c550e6aabcce3e71e2c153778a25a15cf98798eb946b960342e5d9fb9

Observation c024524d-fe3f-4ca8-a830-cc84a90f3fcb · outbound

This paper cites Einfache Beweise der isoperimetrischen H auptsätze.

Free energy minimizers with radial densities: classification and quantitative stability Einfache Beweise der isoperimetrischen H auptsätze

Reference 66

Resolution
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source=pdf_text observed=2026-08-11T22:02:08.211062Z digest=sha256:51ce5ffbb8472ed231927ab1b57d206d512afde15d4147e36b8c2fa917979992

Observation 14d397c4-3112-4af0-93c4-f9c8d26486ff · outbound

This paper cites On the sphericity of liquid droplets.

Free energy minimizers with radial densities: classification and quantitative stability On the sphericity of liquid droplets

Reference 67

Resolution
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source=pdf_text observed=2026-08-11T22:02:08.218685Z digest=sha256:4d00b620e9193bd78beada74a4b895602697ae91e783a419ccf93533a9c09065

Observation dcc74a6e-19ee-4b29-bedd-3073dc707421 · outbound

This paper cites The spaces BV and quasilinear equation s.

Free energy minimizers with radial densities: classification and quantitative stability The spaces BV and quasilinear equation s

Reference 68

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source=pdf_text observed=2026-08-11T22:02:08.237182Z digest=sha256:74d7c09724657d3ac3d8bf9c7ed29a23e8feb5cef298482f8816bf8419a92110

Observation 70502dc1-6ed0-4e05-8124-531f7a4e1fdd · outbound

This paper cites The symmetry of sessile and pendent drops.

Free energy minimizers with radial densities: classification and quantitative stability The symmetry of sessile and pendent drops

Reference 69

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source=pdf_text observed=2026-08-11T22:02:08.245459Z digest=sha256:c4ddf6542cde3905d8708e8a706a8e4743b150de3d881aa19d5a9d277da0c300

Pith citing papers

Observation b9322bd9-39fb-4655-babd-04033520be94 · inbound

The one-dimensional equilibrium shape of a crystal cites this paper.

The one-dimensional equilibrium shape of a crystal Free energy minimizers with radial densities: classification and quantitative stability

Reference 1

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local_arxiv, observed 2026-08-10T20:37:39.913538Z

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source=arxiv_source observed=2026-08-10T20:37:39.747038Z digest=sha256:f22e7c74baa0027ad88e4c4d625e5c4d67db2c5cf82b87726a887af2708fb66a