On the isolated singularities of the solutions of the Gaussian curvature equation for nonnegative curvature

TL;DR

This paper characterizes the precise asymptotic behavior of solutions to a 2D Gaussian curvature equation with nonnegative curvature near isolated singularities, providing detailed insights into their singularity structure.

Contribution

It offers a detailed asymptotic analysis of solutions to the Gaussian curvature equation near isolated singularities for nonnegative curvature functions.

Findings

Exact asymptotic behavior near singularities

Characterization of solutions with bounded nonnegative curvature

Insights into the structure of solutions with finite total curvature

Abstract

The precise asymptotic behaviour of the solutions to the twodimensional curvature equation $\Delta u=k(z) e^{2 u}$ with $e^{2 u} \in L^1$ for bounded nonnegative curvature functions $-k(z)$ near isolated singularities is obtained.