Stability of capillary hypersurfaces in a Euclidean ball

Haizhong Li and Changwei Xiong

Vol. 297 (2018), No. 1, 131–146

DOI: 10.2140/pjm.2018.297.131

Abstract

We study the stability of capillary hypersurfaces in a unit Euclidean ball. It is proved that if the center of mass of the domain 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. We also conjecture a precise delineation of the stable capillary hypersurfaces in unit Euclidean balls.

Keywords

capillary hypersurface, instability, spherical boundary

Mathematical Subject Classification 2010

Primary: 49Q10, 53A10

Milestones

Received: 5 July 2016

Revised: 5 September 2017

Accepted: 23 March 2018

Published: 7 October 2018