Mean field equation of liouville type with singular data: Topological degree
Journal
Communications on Pure and Applied Mathematics
Journal Volume
68
Journal Issue
6
Pages
887-947
Date Issued
2015
Author(s)
Abstract
We consider the following mean field equation: Δgv+ρ(h*ev∫Mh*ev-1)=4π∑j=1Nαj(δqj-1) on M, where M is a compact Riemann surface with volume 1, h* is a positive C1 function on M, and ρ and αj are constants satisfying αj>-1. In this paper, we derive the topological-degree-counting formula for noncritical values of ρ. 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.
Type
journal article