Local and global visibility and Gromov hyperbolicity of domains with respect to the Kobayashi distance - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Transactions of the American Mathematical Society Année : 2023

Local and global visibility and Gromov hyperbolicity of domains with respect to the Kobayashi distance

Résumé

We introduce the notion of locally visible and locally Gromov hyperbolic domains in C d \mathbb {C}^d . We prove that a bounded domain in C d \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.
Fichier principal
Vignette du fichier
local-vis-sub-TAMS-revised_v2.pdf (237.25 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Licence : CC BY NC ND - Paternité - Pas d'utilisation commerciale - Pas de modification

Dates et versions

hal-04285686 , version 1 (14-11-2023)

Identifiants

Citer

Filippo Bracci, Hervé Gaussier, Nikolai Nikolov, Pascal Thomas. Local and global visibility and Gromov hyperbolicity of domains with respect to the Kobayashi distance. Transactions of the American Mathematical Society, 2023, 377 (1), pp.471--493. ⟨10.1090/tran/9010⟩. ⟨hal-04285686⟩
56 Consultations
14 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More