Mean Field Equation of Liouville Type with Singular Data: Topological Degree

被引：71

作者：

Chen, Chiun-Chuan ^{[1
]}

Lin, Chang-Shou ^{[2
]}

机构：

[1] Natl Taiwan Univ, Natl Ctr Theoret Sci, Taipei 10617, Taiwan

[2] Natl Taiwan Univ, Taida Inst Math Sci, Ctr Adv Study Theoret Sci, Taipei 10617, Taiwan

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2015年 / 68卷 / 06期

关键词：

BLOW-UP SOLUTIONS; 2-DIMENSIONAL EULER EQUATIONS; STATISTICAL-MECHANICS; ELECTROWEAK THEORY; CONDENSATE SOLUTION; CONFORMAL METRICS; STATIONARY FLOWS; EXISTENCE; INEQUALITY; CURVATURE;

D O I：

10.1002/cpa.21532

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the following mean field equation: (qj-1)onM, where M is a compact Riemann surface with volume 1, h* is a positive C-1 function on M, and and (j) are constants satisfying (j)>-1. In this paper, we derive the topological-degree-counting formula for noncritical values of . We also give several applications of this formula, including existence of the curvature +1 metric with conic singularities, doubly periodic solutions of electroweak theory, and a special case of self-gravitating strings. (c) 2015 Wiley Periodicals, Inc.

引用

页码：887 / 947

页数：61

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