Spacelike radial graphs of prescribed mean curvature in the Lorentz-Minkowski space

TL;DR

This paper studies the existence and uniqueness of spacelike radial graphs with prescribed mean curvature in Lorentz-Minkowski space, focusing on boundary conditions on hyperbolic space.

Contribution

It establishes conditions for existence and uniqueness of such graphs, extending the understanding of geometric PDEs in Lorentzian geometry.

Findings

Proves existence of spacelike radial graphs with prescribed mean curvature

Establishes uniqueness under certain boundary conditions

Provides new insights into geometric PDEs in Lorentzian manifolds

Abstract

In this paper we investigate the existence and uniqueness of spacelike radial graphs of prescribed mean curvature in the Lorentz-Minkowski space $\mathbb{L}^{n+1}$, for $n\geq 2$, spanning a given boundary datum lying on the hyperbolic space $\mathbb{H}^n$.