An integral equation in conformal geometry

Fengbo Hang; Xiaodong Wang; Xiaodong Yan

doi:10.1016/j.anihpc.2007.03.006

An integral equation in conformal geometry

Fengbo Hang, Xiaodong Wang, Xiaodong Yan

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	1-21
Number of pages	21
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	26
Issue number	1
DOIs	https://doi.org/10.1016/j.anihpc.2007.03.006
State	Published - 2009

Keywords

Isoperimetric inequalities
Poisson kernel
Yamabe type integral equations

ASJC Scopus subject areas

Analysis
Mathematical Physics
Applied Mathematics

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10.1016/j.anihpc.2007.03.006

Cite this

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title = "An integral equation in conformal geometry",

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.",

keywords = "Isoperimetric inequalities, Poisson kernel, Yamabe type integral equations",

author = "Fengbo Hang and Xiaodong Wang and Xiaodong Yan",

note = "Funding Information: The research of F. Hang is supported by National Science Foundation Grant DMS-0647010 and a Sloan Research Fellowship. The research of X. Wang is supported by National Science Foundation Grant DMS-0505645. The research of X. Yan is supported by National Science Foundation Grant DMS-0401048. We would like to thank Professor R. Mazzeo and Professor E. Stein for some helpful discussions. We also thank the referee for his/her careful reading of the original manuscript.",

year = "2009",

doi = "10.1016/j.anihpc.2007.03.006",

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T1 - An integral equation in conformal geometry

AU - Hang, Fengbo

AU - Wang, Xiaodong

AU - Yan, Xiaodong

N1 - Funding Information: The research of F. Hang is supported by National Science Foundation Grant DMS-0647010 and a Sloan Research Fellowship. The research of X. Wang is supported by National Science Foundation Grant DMS-0505645. The research of X. Yan is supported by National Science Foundation Grant DMS-0401048. We would like to thank Professor R. Mazzeo and Professor E. Stein for some helpful discussions. We also thank the referee for his/her careful reading of the original manuscript.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Isoperimetric inequalities

KW - Poisson kernel

KW - Yamabe type integral equations

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JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

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ER -

An integral equation in conformal geometry

Abstract

Keywords

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