Vol. 297, No. 1, 2018

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ISSN: 0030-8730
Stability of capillary hypersurfaces in a Euclidean ball

Haizhong Li and Changwei Xiong

Vol. 297 (2018), No. 1, 131–146
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
Authors
Haizhong Li
Department of Mathematical Sciences
Tsinghua University
Beijing
China
Changwei Xiong
Mathematical Sciences Institute
Australian National University
Canberra
Australia