Potential theory and applications in conformal geometry

TL;DR

This paper explores the use of potential theory to analyze linear and nonlinear equations in conformal geometry, providing new insights into singularity behavior and geometric properties across dimensions.

Contribution

It offers a comprehensive exposition of recent advances in potential theory applications to conformal geometry, including new theorems and dimension estimates.

Findings

Asymptotic behavior near singularities established

Huber's type theorems derived in conformal geometry

Hausdorff dimension estimates of ends obtained

Abstract

In this paper, we want to give an exposition of our recent work on linear and nonlinear potential theory and their applications in conformal geometry. We use potential theory to study linear and quasilinear equations arising from conformal geometry. We establish the asymptotic behavior near singularities and derive applications in conformal geometry. In particular, we establish some Huber's type theorems and Hausdorff dimension estimates of the ends in conformal geometry in general dimensions.