An integral equation in conformal geometry

Fengbo Hang, Xiaodong Wang, Xiaodong Yan

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1-21
Number of pages21
JournalAnnales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis
Volume26
Issue number1
DOIs
StatePublished - Jan 2009

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Conformal Geometry
Scalar Curvature
Integral equations
Integral Equations
Metric
Isoperimetric
Isoperimetric Inequality
Geometry
Manifolds with Boundary
Zero
Compact Manifold
Class

Keywords

  • Isoperimetric inequalities
  • Poisson kernel
  • Yamabe type integral equations

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics

Cite this

An integral equation in conformal geometry. / Hang, Fengbo; Wang, Xiaodong; Yan, Xiaodong.

In: Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis, Vol. 26, No. 1, 01.2009, p. 1-21.

Research output: Contribution to journalArticle

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