The Dirichlet problem for a class of Hessian quotient equations in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$

TL;DR

This paper establishes existence and uniqueness results for a class of Hessian quotient equations with Dirichlet boundary conditions in Lorentz-Minkowski space, contributing to prescribed curvature problems in differential geometry.

Contribution

It extends the theory of Hessian quotient equations to Lorentz-Minkowski space, providing new existence and uniqueness results under suitable conditions.

Findings

Proved existence of solutions under certain boundary conditions

Established uniqueness of solutions in Lorentz-Minkowski space

Connected the results to prescribed curvature problems

Abstract

In this paper, under suitable settings, we can obtain the existence and uniqueness of solutions to a class of Hessian quotient equations with Dirichlet boundary condition in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$, which can be seen as a prescribed curvature problem and a continuous work of [12].