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 $\Delta u=k(z)e^{2u}$ with $e^{2u}\in L^1$ for bounded nonnegative curvature functions $-k(z)$ near isolated singularities is obtained.

References in corpus (1)

• The behaviour of solutions of the Gaussian curvature equation near an isolated boundary point

Cited by in corpus (3)

• Variants of Ahlfors' lemma and properties of the logarithmic potentials
• Metrics with conical singularities on the sphere and sharp extensions of the theorems of Landau and Schottky
• Asymptotic properties of the hyperbolic metric on the sphere with three conical singularities