Removable and essential singular sets for higher dimensional conformal maps

Details Removable and essential singular sets for higher dimensional conformal maps Removable and essential singular sets for higher dimensional conformal maps

2011-10-05

arxiv.org/abs/1110.0898v1

Mathematics

Differential Geometry

44 pages

Scientific paper

In this article, we prove several results about the extension to the boundary of conformal immersions from an open subset $\Omega$ of a Riemannian manifold $L$, into another Riemannian manifold $N$ of the same dimension. In dimension $n \geq 3$, and when the $(n-1)$-dimensional Hausdorff measure of $\partial \Omega$ is zero, we completely classify the cases when $\partial \Omega$ contains essential singular points, showing that $L$ and $N$ are conformally flat and making the link with the theory of Kleinian groups.

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