Uniqueness of conformal metrics with prescribed total curvature in R2
Journal
Calculus of Variations and Partial Differential Equations
Journal Volume
10
Journal Issue
4
Pages
291-319
Date Issued
2000
Author(s)
Abstract
In this paper, we investigate the solution structure of solutions of (0.1) Δu(cursive Greek chi) + K(cursive Greek chi)e2u = 0 in R2, where K(cursive Greek chi) is a Hölder function in R2. For a given positive total curvature, we consider the problem of the uniqueness of solutions with this prescribed total curvature. We apply various methods such as the method of moving spheres and the isoperimetric inequality to show the uniqueness for several classes of K.
Type
journal article