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An integral equation in conformal geometry

Fengbo Hang·Xiaodong Wang·Xiaodong Yan
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Abstract

We study the existence of a metric with zero scalar curvature maximizing the isoperimetric ratio among all zero scalar curvature metrics in a fixed conformal class of metrics on a compact manifold with boundary. The question may be reduced to an extremal problem for the harmonic extension of functions and the related nonlinear integral equation is discussed.

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Fengbo Hang, Xiaodong Wang, Xiaodong Yan. 2007-03-27. An integral equation in conformal geometry. https://arxiv.org/abs/math/0703821

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