An integral equation in conformal geometry
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🧮 math.AP
math.DG
keywords
conformalcurvatureequationintegralmetricsscalarzeroboundary
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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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