Liouville—Ttype Theorems for Conformal Gaussian Curvature Equations in R^2 Liouville-Type Theorems for Conformal Gaussian Curvature Equations in <Emphasis Type="Italic">R</Emphasis><Superscript>2</Superscript>期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Liouville—Ttype Theorems for Conformal Gaussian Curvature Equations in R^2

引用本文：

YunYanYANG. Liouville—Ttype Theorems for Conformal Gaussian Curvature Equations in R^2[J]. 数学学报(英文版), 2003, 19(1): 63-68. DOI: 10.1007/s10114-002-0227-1

作者姓名：

YunYanYANG

作者单位：

LMAM,SchoolofMathematicalSciences,PekingUniversity,Beijing100871

摘要：

In this paper,we derive an elementary identity for smooth solutions of the following equation:△u(x) K(x)e^2u(x)=0 in R^2 and use it to get some global properties of the solutions.

关键词：

刘维尔型定理全曲率 Obata型恒等式共形高斯曲率方程光滑解

Liouville-Type Theorems for Conformal Gaussian Curvature Equations in R2

Yun?Yan?YangEmail author. Liouville-Type Theorems for Conformal Gaussian Curvature Equations in R2[J]. Acta Mathematica Sinica(English Series), 2003, 19(1): 63-68. DOI: 10.1007/s10114-002-0227-1

Authors:

Yun?Yan?Yang mailto:yangyy@math.pku.edu.cn" title=" yangyy@math.pku.edu.cn" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author

Affiliation:

(1) LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China

Abstract:

In this paper, we derive an elementary identity for smooth solutions of the following equation:

$Delta uleft( x right) + Kleft( x right)e^{2uleft( x right)} = 0,{rm in},R^2$

and use it to get some global properties of the solutions.

Keywords:

Gaussian curvature Total curvature Obata-type identity

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