The Dirichlet Problem for Curvature Equations in Riemannian Manifolds

TL;DR

This paper establishes the existence of classical solutions to curvature-based fully nonlinear elliptic equations on Riemannian manifolds, extending previous results to broader curvature functions and less convex domains.

Contribution

It introduces new second derivative boundary estimates enabling the extension of classical existence theorems to more general curvature functions and less convex domains.

Findings

Proved existence of solutions for a class of curvature equations.

Derived new boundary estimates for second derivatives.

Extended classical theorems to broader curvature functions.

Abstract

We prove the existence of classical solutions to the Dirichlet problem for a class of fully nonlinear elliptic equations of curvature type on Riemannian manifolds. We also derive new second derivative boundary estimates which allows us to extend some of the existence theorems of Caffarelli, Nirenberg and Spruck [4] and Ivochkina, Trundinger and Lin [19] to more general curvature functions and less convex domains.