GAUSSIAN CURVATURE ON SINGULAR SURFACES

被引:18
|
作者
CHEN, WX
LI, CM
机构
[1] SW MISSOURI STATE UNIV,DEPT MATH,SPRINGFIELD,MO 65804
[2] INST ADV STUDY,SCH MATH,PRINCETON,NJ 08540
关键词
CRITICAL AND SUPERCRITICAL CASES; NONLINEAR ELLIPTIC EQUATIONS; VARIATIONAL METHODS; PRESCRIBING GAUSSIAN CURVATURE; SURFACES WITH CONICAL SINGULARITIES;
D O I
10.1007/BF02921316
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider prescribing Gaussian curvature on surfaces with conical singularities in both Then we obtain sufficient conditions for a function to be the Gaussian curvature of some pointwise conformal singular metric. We only require that the values of the function are not too large at singular points of the metric with the smallest angle, say, less or equal to 0, or less than its average value. To prove the results, we apply some new ideas and techniques. One of them is to estimate the total curvature along a certain minimizing sequence by using the ''Distribution of Mass Principle'' and the behavior of the critical points at infinity.
引用
收藏
页码:315 / 334
页数:20
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