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

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

2002-08-13

arxiv.org/abs/math/0208101v1

Mathematics

Analysis of PDEs

Scientific paper

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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