A Riemann Mapping Type Theorem in Higher Dimensions, Part I: The Conformally Flat Case with Umbilic Boundary
Mohameden Ould Ahmedou · Birkhäuser Basel eBooks · 2003
In this paper we prove that every Riemannian metric on a locally conformally flat manifold with umbilic boundary can be conformally deformed to a 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.