A class of prescribed Weingarten curvature equations in Euclidean space

TL;DR

This paper studies a specific class of curvature equations in Euclidean space, establishing existence results under certain conditions using degree theory and a priori estimates.

Contribution

It introduces new existence results for prescribed Weingarten curvature equations using degree theory and a priori estimates.

Findings

Existence of solutions under certain conditions

Application of degree theory to curvature equations

Development of a priori estimates for solutions

Abstract

In this paper, we consider a class of prescribed Weingarten curvature equations. Under some sufficient condition, we obtain an existence result by the standard degree theory based on the a prior estimates for the solutions to the prescribed Weingarten curvature equations.