Conformal Killing graphs with prescribed mean curvature

TL;DR

This paper establishes the existence and uniqueness of conformal Killing graphs with specified mean curvature in a broad class of Riemannian manifolds, including those with a conformal Killing vector field.

Contribution

It introduces new existence and uniqueness results for prescribed mean curvature graphs in manifolds with conformal Killing vector fields.

Findings

Proved existence of prescribed mean curvature graphs.

Established uniqueness in a broad class of Riemannian manifolds.

Included manifolds with conformal Killing vector fields.

Abstract

We prove the existence and uniqueness of graphs with prescribed mean curvature function in a large class of Riemannian manifolds which comprises spaces endowed with a conformal Killing vector field.