全平面上的高斯曲率方程

Gaussian Curvature Equation on the Whole Plane

本文用Ｓｃｈａｕｄｅｒ不动点定理证明了一维Ｋ≥０的解、二维Ｋ≥０的径向解的存在性，同时证明了当Ｋ≤０时，在无穷远处有不同渐近性的Ｋ所对应的极大解的渐近性，并给出了径向解的刻画，推广了前人结果．

In this paper, the existences of solutions for K≥0 in one dimension and radial solutions for K≥0 in two dimensions are proved by the Schauder′s fixed point theorem. Moreover, the asymptotic behavior of the maximal solution is described and the radial solutions are classified for K≤0 and has appropriate asympototic behavior at infinite distance.