Local and global visibility and Gromov hyperbolicity of domains with respect to the Kobayashi distance
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- by Filippo Bracci, Hervé Gaussier, Nikolai Nikolov and Pascal J. Thomas
- Trans. Amer. Math. Soc. 377 (2024), 471-493
- DOI: https://doi.org/10.1090/tran/9010
- Published electronically: October 19, 2023
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Abstract:
We introduce the notion of locally visible and locally Gromov hyperbolic domains in $\mathbb {C}^d$. We prove that a bounded domain in $\mathbb {C}^d$ is locally visible and locally Gromov hyperbolic if and only if it is (globally) visible and Gromov hyperbolic with respect to the Kobayashi distance. This allows to detect, from local information near the boundary, those domains which are Gromov hyperbolic and for which biholomorphisms extend continuously up to the boundary.References
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Bibliographic Information
- Filippo Bracci
- Affiliation: Dipartimento Di Matematica, Università di Roma “Tor Vergata”, Via Della Ricerca Scientifica 1, 00133, Roma, Italy
- MR Author ID: 631111
- Email: fbracci@mat.uniroma2.it
- Hervé Gaussier
- Affiliation: Univ. Grenoble Alpes, IF, F-38000 Grenoble, France and CNRS, IF, F-38000 Grenoble, France
- ORCID: 0000-0001-6605-6064
- Email: herve.gaussier@univ-grenoble-alpes.fr
- Nikolai Nikolov
- Affiliation: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Block 8, 1113 Sofia, Bulgaria; and Faculty of Information Sciences, State University of Library Studies and Information Technologies, 69A, Shipchenski prohod Str., 1574 Sofia, Bulgaria
- MR Author ID: 332842
- Email: nik@math.bas.bg
- Pascal J. Thomas
- Affiliation: Institut de Mathématiques de Toulouse; UMR5219, Université de Toulouse; CNRS, UPS, F-31062 Toulouse Cedex 9, France
- MR Author ID: 238303
- ORCID: 0000-0002-9365-3398
- Email: pascal.thomas@math.univ-toulouse.fr
- Received by editor(s): March 1, 2022
- Received by editor(s) in revised form: March 13, 2023
- Published electronically: October 19, 2023
- Additional Notes: The first author was partially supported by PRIN 2017 Real and Complex Manifolds: Topology, Geometry and holomorphic dynamics, Ref: 2017JZ2SW5, by GNSAGA of INdAM and by the MUR Excellence Department Project MatMod@TOV CUP:E83C23000330006 awarded to the Department of Mathematics, University of Rome Tor Vergata
The second author was partially supported by ERC ALKAGE
The third author was partially supported by the National Science Fund, Bulgaria under grant number KP-06-N52/3. - © Copyright 2023 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 377 (2024), 471-493
- MSC (2020): Primary 32F45
- DOI: https://doi.org/10.1090/tran/9010
- MathSciNet review: 4684599