Existence of nonparametric solutions for a capillary problem in warped products

Jorge H. Lira and Gabriela A. Wanderley

Vol. 269 (2014), No. 2, 407–424

DOI: 10.2140/pjm.2014.269.407

Abstract

We prove that there exist solutions for a nonparametric capillary problem in a wide class of Riemannian manifolds endowed with a Killing vector field. In other terms, we prove the existence of Killing graphs with prescribed mean curvature and prescribed contact angle along its boundary. These results may be useful for modeling stationary hypersurfaces under the influence of a nonhomogeneous gravitational field defined over an arbitrary Riemannian manifold.

Keywords

capillary, mean curvature, Killing graphs

Mathematical Subject Classification 2010

Primary: 53C42, 53C21

Milestones

Received: 2 May 2013

Revised: 26 November 2013

Accepted: 16 December 2013

Published: 26 July 2014