An integral equation in conformal geometry

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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.
23 pages

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Analysis of PDEs, Differential Geometry, 45G05, 53A30

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http://salesiana.dossiersoluciones.com/handle/123456789/126528

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0703821
 http://arxiv.org/abs/math/0703821

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arXiv