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Abstract Boundaries and Continuous Extension of Biholomorphisms

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Abstract

We present different constructions of abstract boundaries for bounded complete (Kobayashi) hyperbolic domains in ℂd, d ≥ 1. These constructions essentially come from the geometric theory of metric spaces. We also present, as an application, some extension results concerning biholomorphic maps.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1, 00133, Roma, Italy

    F. Bracci

  2. Université Grenoble Alpes, 38402, Grenoble, France

    H. Gaussier

Authors
  1. F. Bracci
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  2. H. Gaussier
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Correspondence to F. Bracci.

Additional information

To Professor László Lempert for his 70th birthday

Partially supported by PRIN 2017 Real and Complex Manifolds: Topology, Geometry and holomorphic dynamics, Ref: 2017JZ2SW5, by GNSAGA of INdAM and by the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006.

Partially supported by ERC ALKAGE.

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Bracci, F., Gaussier, H. Abstract Boundaries and Continuous Extension of Biholomorphisms. Anal Math 48, 393–409 (2022). https://doi.org/10.1007/s10476-022-0163-5

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  • DOI: https://doi.org/10.1007/s10476-022-0163-5

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