JournalscmhVol. 89, No. 2pp. 405–441

Removable and essential singular sets for higher dimensional conformal maps

  • Charles Frances

    Université Paris Sud, Orsay, France
Removable and essential singular sets for higher dimensional  conformal maps cover
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Abstract

In this article, we prove several results about the extension to the boundary of conformal immersions from an open subset Ω\Omega of a Riemannian manifold LL into another Riemannian manifold NN of the same dimension. In dimension n3n \geq 3, and when the (n1)(n-1)-dimensional Hausdorff measure of Ω\partial \Omega is zero, we completely classify the cases when Ω\partial \Omega contains essential singular points, showing that LL and NN 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. 405–441

DOI 10.4171/CMH/323