The Dirichlet problem for a class of curvature equations in Minkowski space

TL;DR

This paper addresses the existence of smooth spacelike hypersurfaces with prescribed curvature in Minkowski space by establishing a priori $C^2$ estimates for solving the Dirichlet problem.

Contribution

It introduces new methods to prove existence results for curvature equations in Minkowski space with general boundary conditions.

Findings

Existence of smooth spacelike hypersurfaces with prescribed curvature.

Development of a priori $C^2$ estimates for the problem.

Extension to general boundary data.

Abstract

In this paper, we study the Dirichlet problem for a class of prescribed curvature equations in Minkowski space. We prove the existence of smooth spacelike hypersurfaces with a class of prescribed curvature and general boundary data based on establishing the \emph{a priori} $C^2$ estimates.