Compactness and Finiteness Results for Gromov-Hyperbolic Spaces

Gérard Besson () and Gilles Courtois ()
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Gérard Besson: Université de Grenoble, Institut Fourier
Gilles Courtois: Institut de Mathématiques de Jussieu – Paris Rive Gauche (IMJ-PRG)

Chapter Chapter 6 in Surveys in Geometry I, 2022, pp 205-268 from Springer

Abstract: Abstract This is a series of lectures on Bishop–Gromov’s type inequalities adapted to metric spaces. We consider the case of Gromov-hyperbolic spaces and draw consequences of these inequalities such as compactness and finiteness Theorems. This course is intended to be elementary in the sense that the necessary background is described in detail.

Keywords: Gromov-hyperbolic space; Bishop–Gromov inequalities; Comparison theorems; Entropy; Ricci curvature; Compactness theorems in metric spaces; Finiteness theorems i metric spaces; Gromov–Hausdorff topology; 51K10; 53C23; 53C21; 53E20; 57K30 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-86695-2_6

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DOI: 10.1007/978-3-030-86695-2_6

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