Strong hyperbolicity

DOI10.4171/GGD/372zbMath1368.20057arXiv1408.0250OpenAlexW3037230926MaRDI QIDQ329568

Ján Špakula, Bogdan Nica

Publication date: 21 October 2016

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.0250

zbMATH Keywords

harmonic measurehyperbolic groupCAT(\(-1\)) spaceGreen metric

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Hyperbolic groups and nonpositively curved groups (20F67)

Related Items (14)

Relating boundary and interior solutions of the cohomological equation for cocycles by isometries of negatively curved spaces. The Lǐsic case* ⋮ Hyperbolization of the limit sets of some geometric constructions ⋮ Ptolemy Through the Centuries ⋮ The Four Point Condition: An Elementary Tropicalization of Ptolemy’s Inequality ⋮ The space of metric structures on hyperbolic groups ⋮ Growth of some hyperbolic type distances and starlikeness of metric balls ⋮ Topological flows for hyperbolic groups ⋮ Two applications of strong hyperbolicity ⋮ Entropy and drift for word metrics on relatively hyperbolic groups ⋮ Strongly hyperbolic metrics on Ptolemy spaces ⋮ A new intrinsic metric on metric spaces ⋮ Hyperbolic metrics on open subsets of Ptolemaic spaces with sharp parameter bounds ⋮ Some spherical functions on hyperbolic groups ⋮ The quasi-hyperbolicity constant of a metric space

Cites Work

• Hyperbolicity, CAT(\(-1\))-spaces and the Ptolemy inequality
• Internal diffusion limited aggregation on discrete groups having exponential growth
• Bivariant \(K\)-theory for Banach algebras and the Baum-Connes conjecture
• The Baum-Connes conjecture for hyperbolic groups.
• Embeddings of Gromov hyperbolic spaces
• Conformal structure on the boundary and geodesic flow of a \(\text{CAT}(-1)\)-space
• Central limit theorems for Gromov hyperbolic groups
• Flows and joins of metric spaces
• Local limit theorem for symmetric random walks in Gromov-hyperbolic groups
• Proper isometric actions of hyperbolic groups on -spaces
• Harmonic measures versus quasiconformal measures for hyperbolic groups
• Metric conformal structures and hyperbolic dimension

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