Stability of capillary hypersurfaces in a Euclidean ball

TL;DR

This paper investigates the stability of capillary hypersurfaces within a Euclidean ball, establishing conditions under which these surfaces are unstable, and showing most known examples are unstable except for specific cases.

Contribution

It provides a new criterion linking the mass center position to the stability of capillary hypersurfaces, expanding understanding of their stability properties.

Findings

Most known capillary hypersurfaces are unstable

Stability depends on the mass center location

Totally geodesic and spherical caps are stable

Abstract

We study the stability of capillary hypersurfaces in a unit Euclidean ball. It is proved that if the mass center of the generalized body enclosed by the immersed capillary hypersurface and the wetted part of the sphere is located at the origin, then the hypersurface is unstable. An immediate result is that all known examples except the totally geodesic ones and spherical caps are unstable.