Removable and essential singular sets for higher dimensional conformal maps

In this article, we prove several results about the extension to the boundary of conformal immersions from an open subset $Ω$ 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 $\partial Ω$ is zero, we completely classify the cases when $\partial Ω$ 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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