On Fully Nonlinear Loewner-Nirenberg Problem of Ricci curvature

TL;DR

This paper establishes the existence of smooth, complete conformal metrics with prescribed negative Ricci curvature conditions, extending to more general equations in Euclidean domains.

Contribution

It proves the existence of such metrics for the fully nonlinear Loewner-Nirenberg problem and generalizes the formulation to broader equations.

Findings

Existence of smooth complete conformal metrics with prescribed negative Ricci curvature.

Extension of the problem to more general nonlinear equations.

Framework applicable to general domains in Euclidean space.

Abstract

We prove the existence of a smooth complete conformal metric with prescribed kth elementary symmetric function of negative Ricci curvature under certain condition on general domain in Euclidean space. We then formulate this problem for more general equations.