A1 Journal article (refereed)
Conformal equivalence of visual metrics in pseudoconvex domains (2020)

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

JYU authors or editors

Publication details

All authors or editors: Capogna, Luca; Le Donne, Enrico

Journal or series: Mathematische Annalen

ISSN: 0025-5831

eISSN: 1432-1807

Publication year: 2020

Volume: 377

Issue number: 3-4

Pages range: 1643-1672

Publisher: Springer

Publication country: Germany

Publication language: English

DOI: https://doi.org/10.1007/s00208-020-01968-9

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/67969

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1703.00238

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.

Keywords: complex-valued functions; differential geometry

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 2