A Riemannian mapping type Theorem in higher dimensions, Part I: the conformally flat case with umbilic boundary

2002/08/13 by Mohameden Ould Ahmedou, Ahmedou, Mohameden Ould
Mathematics · #35J60 #53C21 #58G30 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG #msc:35J60 #msc:53C21 #msc:58G30

paper · pdf · doi:10.48550/arxiv.math/0208101

arxiv created 2002/08/13 · arxiv updated 2009/11/30

Abstract

In this paper we prove that every Riemannian metric on a locally conformally flat manifold with umbilic boundary can be conformally deformed to a scalar flat metric having constant mean curvature. This result can be seen as a generalization to higher dimensions of the well known Riemann mapping Theorem in the plane.

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