An integral equation in conformal geometry

Details An integral equation in conformal geometry An integral equation in conformal geometry

2007-03-27

arxiv.org/abs/math/0703821v1

Mathematics

Analysis of PDEs

23 pages

Scientific paper

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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