The isoperimetric inequality for the capillary energy outside convex cylinders

Nicola Fusco; Vesa Julin; Massimiliano Morini

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arXiv · 2406.19011

The isoperimetric inequality for the capillary energy outside convex cylinders

Nicola Fusco·Vesa Julin·Massimiliano Morini

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Abstract

We study the isoperimetric problem for capillary surfaces with a general contact angle $\theta \in (0, \pi)$, outside convex infinite cylinders with arbitrary two-dimensional convex section. We prove that the capillary energy of any surface supported on any such convex cylinder is strictly larger than that of a spherical cap with the same volume and the same contact angle on a flat support, unless the surface is itself a spherical cap resting on a facet of the cylinder. In this class of convex sets, our result extends for the first time the well-known Choe-Ghomi-Ritor\'e relative isoperimetric inequality, corresponding to the case $\theta = \pi/2$, to general angles.

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Nicola Fusco, Vesa Julin, Massimiliano Morini. 2024-06-27. The isoperimetric inequality for the capillary energy outside convex cylinders. https://arxiv.org/abs/2406.19011

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