Geometric quantities arising from bubbling analysis of mean field equations
Journal
Communications in Analysis and Geometry
Journal Volume
28
Journal Issue
6
Pages
1289-1313
Date Issued
2020
Author(s)
Lin C.-S
Abstract
Let E = C/Λ be a flat torus and G be its Green function with singularity at 0. Consider the multiple Green function Gn on En: n Gn(z1, . . ., zn):= X G(zi ? zj) ? n X G(zi). i<j i=1 A critical point a = (a1, . . ., an) of Gn is called trivial if {a1, . . ., an} = {?a1, . . ., ?an}. For such a point a, two geometric quantities D(a) and H(a) arising from bubbling analysis of mean field equations are introduced. D(a) is a global quantity measuring asymptotic expansion and H(a) is the Hessian of Gn at a. By way of geometry of Lam? curves developed in [3], we derive precise formulas to relate these two quantities. ? 2020 International Press of Boston, Inc.. All rights reserved.
Type
journal article