Saved in:
Bibliographic Details
Main Authors: Fusco, N., Julin, V., Morini, M., Pratelli, A.
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2509.10200
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866916963138142208
author Fusco, N.
Julin, V.
Morini, M.
Pratelli, A.
author_facet Fusco, N.
Julin, V.
Morini, M.
Pratelli, A.
contents We study the isoperimetric problem for capillary hypersurfaces with a general contact angle $θ\in (0, π)$, outside arbitrary convex sets. We prove that the capillary energy of any surface supported on any such convex set is larger than that of a spherical cap with the same volume and the same contact angle on a flat support, and we characterize the equality cases. This provides a complete solution to the isoperimetric problem for capillary surfaces outside convex sets at arbitrary contact angles, generalizing the well-known Choe-Ghomi-Ritoré inequality, which corresponds to the case $θ=\frac\pi2$.
format Preprint
id arxiv_https___arxiv_org_abs_2509_10200
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The isoperimetric inequality for the capillary energy outside convex sets
Fusco, N.
Julin, V.
Morini, M.
Pratelli, A.
Analysis of PDEs
We study the isoperimetric problem for capillary hypersurfaces with a general contact angle $θ\in (0, π)$, outside arbitrary convex sets. We prove that the capillary energy of any surface supported on any such convex set is larger than that of a spherical cap with the same volume and the same contact angle on a flat support, and we characterize the equality cases. This provides a complete solution to the isoperimetric problem for capillary surfaces outside convex sets at arbitrary contact angles, generalizing the well-known Choe-Ghomi-Ritoré inequality, which corresponds to the case $θ=\frac\pi2$.
title The isoperimetric inequality for the capillary energy outside convex sets
topic Analysis of PDEs
url https://arxiv.org/abs/2509.10200