Commentarii Mathematici Helvetici


Full-Text PDF (372 KB) | Metadata | Table of Contents | CMH summary
Volume 89, Issue 2, 2014, pp. 405–441
DOI: 10.4171/CMH/323

Published online: 2014-06-18

Removable and essential singular sets for higher dimensional conformal maps

Charles Frances[1]

(1) Université Paris Sud, Orsay, France

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.

Keywords: Conformal mappings, removable sets

Frances Charles: Removable and essential singular sets for higher dimensional conformal maps. Comment. Math. Helv. 89 (2014), 405-441. doi: 10.4171/CMH/323