Fully nonlinear equations of Krylov type on Riemannian manifolds with negative curvature

TL;DR

This paper studies fully nonlinear Krylov-type equations on negatively curved Riemannian manifolds, establishing a priori estimates and existence results that extend previous work in conformal geometry.

Contribution

It extends existing results by proving new a priori estimates and existence theorems for these equations on negatively curved manifolds.

Findings

Established a priori estimates for solutions.

Proved existence of solutions under certain conditions.

Extended previous results in conformal geometry context.

Abstract

In this paper, we consider fully nonlinear equations of Krylov type on Riemannian manifolds with negative curvature which naturally arise in conformal geometry. Moreover, we prove the a priori estimates for solutions to these equations and establish the existence results. Our results can be viewed as an extension of previous results given by Gursky-Viaclovsky and Li-Sheng.