Local Estimates of Singular Solution to Gaussian Curvature Equation

Abstract

" In this paper, we derive the local estimates of a singular solution near its singular set Z of the Gaussian curvature equation \u0394u(x) + K(x)e^{u(x)} = 0 in \u03a9 \\ Z, in the case that K(x) may be zero on Z, where \u03a9 \u2282 R\u00b2 is a bounded open domain, and Z is a set of finite points."