Curvature estimates for spacelike graphic hypersurfaces in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$

TL;DR

This paper establishes curvature estimates for spacelike graphic hypersurfaces in Lorentz-Minkowski space, enabling the proof of existence for hypersurfaces with prescribed curvature and boundary conditions over convex domains.

Contribution

It provides new curvature estimates and existence results for spacelike hypersurfaces with prescribed Weingarten curvature in Lorentz-Minkowski space.

Findings

Derived curvature bounds for spacelike hypersurfaces

Proved existence of hypersurfaces with prescribed curvature and boundary data

Applied results to hyperbolic space domains

Abstract

In this paper, we can obtain curvature estimates for spacelike admissible graphic hypersurfaces in the $(n+1)$-dimensional Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$, and through which the existence of spacelike admissible graphic hypersurfaces, with prescribed $2$-th Weingarten curvature and Dirichlet boundary data, defined over a strictly convex domain in the hyperbolic plane $\mathscr{H}^{n}(1)\subset\mathbb{R}^{n+1}_{1}$ of center at origin and radius $1$, can be proven.