Stable capillary hypersurfaces in a wedge

Jaigyoung Choe and Miyuki Koiso

Vol. 280 (2016), No. 1, 1–15

DOI: 10.2140/pjm.2016.280.1

Abstract

Let $\Sigma$ be a compact immersed stable capillary hypersurface in a wedge bounded by two hyperplanes in ${ℝ}^{n+1}$. Suppose that $\Sigma$ meets those two hyperplanes in constant contact angles $\ge \pi ∕2$ and is disjoint from the edge of the wedge, and suppose that $\partial \Sigma$ consists of two smooth components with one in each hyperplane of the wedge. It is proved that if $\partial \Sigma$ is embedded for $n=2$, or if each component of $\partial \Sigma$ is convex for $n\ge 3$, then $\Sigma$ is part of the sphere. The same is true for $\Sigma$ in the half-space of ${ℝ}^{n+1}$ with connected boundary $\partial \Sigma$.

Keywords

capillary surface, constant mean curvature, stable

Mathematical Subject Classification 2010

Primary: 49Q10

Secondary: 53A10

Milestones

Received: 4 June 2014

Revised: 18 May 2015

Accepted: 24 May 2015

Published: 28 December 2015