In this article, we prove several results about the extension to the boundary of conformal immersions from an open subset of a Riemannian manifold into another Riemannian manifold of the same dimension. In dimension , and when the -dimensional Hausdorff measure of is zero, we completely classify the cases when contains essential singular points, showing that and are conformally flat and making the link with the theory of Kleinian groups.
Cite this article
Charles Frances, Removable and essential singular sets for higher dimensional conformal maps. Comment. Math. Helv. 89 (2014), no. 2, pp. 405–441DOI 10.4171/CMH/323