Removable and essential singular sets for higher dimensional conformal maps

Charles Frances (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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.

Mots clés: conformal geometry; removable sets

Domaines: Géométrie différentielle [math.DG]

Charles Frances. Removable and essential singular sets for higher dimensional conformal maps. 2011. ⟨hal-00629086⟩