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Show Extension on Boundary of Topological Space is Continuous

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Abstract

We present different constructions of abstract boundaries for bounded complete (Kobayashi) hyperbolic domains in ℂ d , 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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Author information

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

Corresponding author

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

Key words and phrases

  • Gromov hyperbolic space
  • biholomorphism
  • boundary extension

Mathematics Subject Classification

  • 32E35

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Source: https://link.springer.com/article/10.1007/s10476-022-0163-5

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