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 Δu(x) + K(x)e^{u(x)} = 0 in Ω \\ Z, in the case that K(x) may be zero on Z, where Ω ⊂ R² is a bounded open domain, and Z is a set of finite points."