Conformal equivalence of visual metrics in pseudoconvex domains
Abstract
We refine estimates introduced by Balogh and Bonk, to show that the boundary extensions of isometries between smooth strongly pseudoconvex domains in $\C^n$ are conformal with respect to the subRiemannian 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 pseudoconvex domains. The proofs are inspired by Mostow's proof of his rigidity theorem and are based on the asymptotic hyperbolic character of the Kobayashi or Bergman metrics and on the BonkSchramm hyperbolic fillings.
 Publication:

arXiv eprints
 Pub Date:
 March 2017
 arXiv:
 arXiv:1703.00238
 Bibcode:
 2017arXiv170300238C
 Keywords:

 Mathematics  Complex Variables;
 Mathematics  Differential Geometry;
 Mathematics  Metric Geometry;
 32T15;
 32Q45;
 32H40;
 53C23;
 53C17
 EPrint:
 20 pages