Document Type
Article
Publication Date
2-1-2021
Publication Title
Mathematische Annalen
Abstract
We refine estimates introduced by Balogh and Bonk, to show that the boundary extensions of isometries between bounded, smooth strongly pseudoconvex domains in Cn 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 are based on the asymptotic hyperbolic character of the Kobayashi or Bergman metrics and on the Bonk-Schramm hyperbolic fillings.
Volume
379
Issue
1-2
First Page
743
Last Page
763
DOI
10.1007/s00208-020-01962-1
ISSN
00255831
Recommended Citation
Capogna, Luca and Le Donne, Enrico, "Conformal Equivalence of Visual Metrics in Pseudoconvex Domains" (2021). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/123
Comments
Peer reviewed accepted manuscript.