# Conformal equivalence of visual metrics in pseudoconvex domains

@article{Capogna2020ConformalEO, title={Conformal equivalence of visual metrics in pseudoconvex domains}, author={Luca Capogna and Enrico Le Donne}, journal={Mathematische Annalen}, year={2020}, volume={379}, pages={743-763} }

We refine estimates introduced by Balogh and Bonk, to show that the boundary extensions of isometries between bounded, smooth strongly pseudoconvex domains in $${\mathbb {C}}^n$$ C n are conformal with respect to the sub-Riemannian metric induced by the Levi form. As a corollary we obtain an alternative proof of a result of Fefferman on smooth extensions of biholomorphic mappings between bounded smooth pseudoconvex domains. The proofs are inspired by Mostow’s proof of his rigidity theorem and…

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