On the asymptotic behavior of solutions of the conformal Gaussian curvature equations in R2
On the asymptotic behavior of solutions of the conformal Gaussian curvature equations in R2
复制标题
R2中共形高斯曲率方程解的渐近行为
DOI：
10.1007/s002080050068
复制
发表时间：
1997
影响因子：
1.4
通讯作者：
Changshou Lin
中科院分区：
文献类型：
--
作者：
Kuo‐shung Cheng;Changshou Lin
本文研究了方程u+ Ke2u= 0（1.1）在R2中的全解u的渐近性质。（1.1）式产生于寻找黎曼度规的问题，该黎曼度规实现给定函数K为高斯曲率，并且与R2中的标准欧几里德度规共形。我们建议读者参考[CN1]对这个问题的背景和历史的简要描述。对方程（1.1）的研究至少可以追溯到20世纪30年代，但似乎（1.1）的所有解的完整分类直到最近才在[CN1， CN2]和[C]中获得，对于R2中的k50的情况。为了说明[C]中的结果，我们引入数量1 as1= sup
In this paper we study the asymptotic behavior of an entire solution u of the equation u+ Ke2u= 0 (1.1) in R2. Equation (1.1) arises in the problem of finding a Riemannian metric which realizes the given function K as its Gaussian curvature and is conformal to the standard Euclidean metric in R2. We refer the reader to [CN1] for a brief description of the background and the history of this problem. The study of the equation (1.1) dates back to at least 1930’s but it seems that a complete classification of all solutions of (1.1) was obtained only very recently in [CN1, CN2] and [C] for the case of K 5 0 in R2. To state the result in [C], we introduce the quantity 1 as1= sup