Calculus of Variations and Geometric Measure Theory

N. Fusco - V. Julin - M. Morini

The isoperimetric inequality for the capillary energy outside convex cylinders

created by fuscon on 03 Jul 2024


Submitted Paper

Inserted: 3 jul 2024
Last Updated: 3 jul 2024

Year: 2024


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-Ritoré relative isoperimetric inequality, corresponding to the case \( \theta = \pi/2 \), to general angles.