JournalsaihpcVol. 26, No. 1pp. 1–21

An integral equation in conformal geometry

  • Fengbo Hang

    Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544, USA

  • Xiaodong Wang

    Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA

  • Xiaodong Yan

    Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
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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.

Cite this article

Fengbo Hang, Xiaodong Wang, Xiaodong Yan, An integral equation in conformal geometry. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 1, pp. 1–21

DOI 10.1016/J.ANIHPC.2007.03.006