Some existence results to the Dirichlet problem for the minimal hypersurface equation on non mean convex domains of a Riemannian manifold

TL;DR

This paper extends the existence results of minimal hypersurfaces solving the Dirichlet problem from Euclidean space to Riemannian manifolds, broadening the understanding of minimal hypersurfaces in curved spaces.

Contribution

It generalizes Jenkins and Serrin's Euclidean results to Riemannian manifolds, providing new existence theorems for minimal hypersurfaces in non mean convex domains.

Findings

Existence of minimal hypersurfaces in Riemannian manifolds established.

Extension of Euclidean results to curved ambient spaces.

Applicable to non mean convex domains.

Abstract

We prove the existence of minimal hypersurfaces for the Dirichlet that extends a similar result of Jenkins and Serrin in Euclidean Space to Riemannian ambient manifolds