The Dirichlet problem for Hessian quotient type curvature equations in Minkowski space

TL;DR

This paper studies the Dirichlet problem for a class of curvature equations involving Hessian quotients in Minkowski space, establishing existence results through a priori estimates.

Contribution

It introduces new a priori C2 estimates for Hessian quotient curvature equations in Minkowski space, leading to existence results in the non-degenerate case.

Findings

Established a priori C2 estimates for the equations.

Proved existence of solutions under non-degeneracy conditions.

Extended the theory of curvature equations in Minkowski space.

Abstract

In this paper, we consider the Dirichlet problem for a class of prescribed Hessian quotient type curvature equations with homogeneous boundary data in Minkowski space. By establishing the a priori C2 estimates, we obtain the existence result in the non-degenerate case.