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An integral equation in conformal geometry

Authors
Journal
Annales de l Institut Henri Poincare (C) Non Linear Analysis
0294-1449
Publisher
Elsevier
Publication Date
Volume
26
Issue
1
Identifiers
DOI: 10.1016/j.anihpc.2007.03.006
Keywords
  • Isoperimetric Inequalities
  • Poisson Kernel
  • Yamabe Type Integral Equations

Abstract

Abstract Motivated by Carleman's proof of the isoperimetric inequality in the plane, we study the problem of finding a metric with zero scalar curvature maximizing the isoperimetric ratio among all zero scalar curvature metrics in a fixed conformal class on a compact manifold with boundary. We derive a criterion for the existence and make a related conjecture.

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