非负曲率完备2维流形上的共形Gauss曲率方程

Conformal Gaussian curvature equations on the 2-dimensional complete manifolds with nonnegative curvatures

摘要: 研究具有非负Gauss曲率的2维非紧完备黎曼流形上的共形Gauss曲率方程,证明了共形Gauss曲率方程的一般解的存在性与径向对称解的存在性的等价性,得到了涉及共形Gauss曲率方程的径向对称解在无穷远处增长率的一个结果.

Abstract: The conformal Gaussian curvature equation on the 2-dimensional noncompact complete Riemannian manifolds with nonnegative Gaussian curvatures is investigated,the equivalence between the existence of general solutions and that of the radially symmetric solutions is proved,and a result dealing with the growth rate at infinity of the radially symmetric solutions of the conformal Gaussian curvature equation is obtained.