Existence of nonparametric solutions for a capillary problem in warped products

TL;DR

This paper proves the existence of solutions for a non-parametric capillary problem in Riemannian manifolds with Killing vector fields, which could model stationary hypersurfaces under complex gravitational influences.

Contribution

It establishes the existence of Killing graphs with prescribed mean curvature and contact angle in a broad class of Riemannian manifolds, extending previous results.

Findings

Existence of solutions for non-parametric capillary problems in certain manifolds.

Application to modeling hypersurfaces under non-homogeneous gravity.

Extension of classical capillary theory to Riemannian settings.

Abstract

We prove that there exist solutions for a non-parametric 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 modelling stationary hypersurfaces under the influence of a non-homogeneous gravitational field defined over an arbitrary Riemannian manifold.