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An integral equation in conformal geometry. (English) Zbl 1154.45004
Summary: 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.
MSC:
45G05Singular nonlinear integral equations
53A30Conformal differential geometry
References:
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