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 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.
Main Authors
Format
Articles
Research article
Published
2020
Series
Subjects
Publication in research information system
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202002262197Use this for linking
Review status
Peer reviewed
ISSN
0025-5831
DOI
https://doi.org/10.1007/s00208-020-01968-9
Language
English
Published in
Mathematische Annalen
Citation
- Capogna, L., & Le Donne, E. (2020). Conformal equivalence of visual metrics in pseudoconvex domains. Mathematische Annalen, 377(3-4), 1643-1672. https://doi.org/10.1007/s00208-020-01968-9
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Additional information about funding
Open access funding provided by University of Jyväskylä (JYU).
Copyright© Authors, 2020