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