The horofunction boundary of a Gromov hyperbolic space

DOI10.1007/s00208-022-02551-0arXiv2012.09848OpenAlexW3112073010MaRDI QIDQ6191266

Sébastien Gontard, Matteo Fiacchi, Lorenzo Guerini, Leandro Arosio

Publication date: 9 February 2024

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.09848

Mathematics Subject Classification ID

Invariant metrics and pseudodistances in several complex variables (32F45) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50)

Cites Work

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• The horofunction compactification of Teichmüller spaces of surfaces with boundary
• Gromov hyperbolicity and the Kobayashi metric on convex domains of finite type
• Backward iteration in the unit ball
• Some properties of squeezing functions on bounded domains
• Wolff-Denjoy theorems in nonsmooth convex domains
• Characterizing domains by the limit set of their automorphism group
• The Denjoy-Wolff theorem in \(\mathbb C^n\)
• Backward iteration in strongly convex domains
• On laws of large numbers for random walks
• The Lindelöf principle and the angular derivative in strongly convex domains
• Geometry of domains with the uniform squeezing property
• Horospheres and iterates of holomorpic maps
• Géométrie et théorie des groupes. Les groupes hyperboliques de Gromov. (Geometry and group theory. The hyperbolic groups of Gromov)
• Sur les groupes hyperboliques d'après Mikhael Gromov. (On the hyperbolic groups à la M. Gromov)
• Characterization of convex domains with noncompact automorphism group
• The Hilbert metric and Gromov hyperbolicity.
• Gromov hyperbolicity and the Kobayashi metric on strictly pseudoconvex domains
• Random walks on weakly hyperbolic groups
• A proof of the Muir-Suffridge conjecture for convex maps of the unit ball in \(\mathbb{C}^n\)
• A non-strictly pseudoconvex domain for which the squeezing function tends to 1 towards the boundary
• Convex domains of finite type
• Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk
• Canonical models for the forward and backward iteration of holomorphic maps
• Canonical models on strongly convex domains via the squeezing function
• Subelliptic estimates from Gromov hyperbolicity
• Homeomorphic extension of quasi-isometries for convex domains in \(\mathbb{C}^d\) and iteration theory
• Monge-Ampère foliations with singularities at the boundary of strongly convex domains
• Boundaries of hyperbolic metric spaces
• Quelques propriétés des applications analytiques d'une boule à \(m\) dimensions dans elle-même
• Topological mixing in 𝐶𝐴𝑇(-1)-spaces
• Non-expanding maps and Busemann functions
• Properties of squeezing functions and global transformations of bounded domains
• Canonical models for holomorphic iteration
• On conditions under which isometries have bounded orbits
• The horofunction boundary of the Hilbert geometry
• The pluricomplex Poisson kernel for strongly convex domains
• Riemann Surfacese and Related Topics (AM-97)
• La métrique de Kobayashi et la représentation des domaines sur la boule
• Fixed points of commuting holomorphic mappings other than the Wolff point
• Horosphere topology
• Backward orbits in the unit ball
• Gromov hyperbolicity, the Kobayashi metric, and $\mathbb {C}$-convex sets
• Busemann points of infinite graphs

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