方程△g-aKg=0无正函数解的充分条件  

A Sufficient Condition of Nonexistence of Positive Solution of Equation△g-aKg=0

作　　者：徐海峰[1] 

机构地区：[1]扬州大学数学科学学院,扬州225002

出　　处：《数学学报（中文版）》2010年第5期945-952,共8页Acta Mathematica Sinica：Chinese Series

摘　　要：Fischer-Colbrie和Schoen曾在1980年研究过复平面中单位圆盘当赋予某个完备度量时,方程Δg-aKg=0在其上无正函数解的充分条件,并将其结果应用到三维非负数量曲率流形中完备稳定的极小曲面上.这里Δ是Laplace算子,K为高斯曲率,a是常数,g是所讨论的单位圆盘上的函数.本文给出了此方程在该圆盘上无正函数解的一个更弱的充分条件.Fischer-Colbrie and Schoen have studied the equation △g-aKg = 0 on unit disc in complex plane in 1980. The disc is endowed with a complete conformal metric. They got a sufficient condition for the nonexistence of positive solution on such disc and applied this result to the study of complete stable minimal surfaces in 3-dimensional manifolds of non-negative scalar curvature. Here △ is Laplace operator, K is Gauss curvature, a is a constant, and g is a function defined on the unit disc. In this paper, we obtain a more weaker sufficient condition which also ensures the nonexistence of positive solution on such unit disc.

关 键 词：△-q算子 共形度量 高斯曲率 Laplace算子的第一特征值 

分 类 号：O175.23[理学—数学] O186.12[理学—基础数学]