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

Mohameden Ould Ahmedou
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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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Mohameden Ould Ahmedou. 2002-08-13. A Riemannian mapping type Theorem in higher dimensions, Part I: the conformally flat case with umbilic boundary. https://arxiv.org/abs/math/0208101

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