Gromov hyperbolic space | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-05-17

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Hyperbolic_metric_space


00:00:30 1 Definitions
00:01:08 1.1 Definition using the Gromov product
00:04:10 1.2 Definitions using triangles
00:08:45 1.3 Examples
00:09:34 1.4 Hyperbolicity and curvature
00:10:57 2 Important properties
00:12:44 2.1 Invariance under quasi-isometry
00:12:53 2.2 Approximate trees in hyperbolic spaces
00:14:06 2.3 Exponential growth of distance and isoperimetric inequalities
00:17:35 2.4 Quasiconvex subspaces
00:21:19 2.5 Asymptotic cones
00:22:16 3 The boundary of a hyperbolic space
00:22:34 3.1 Definition using the Gromov product
00:23:07 3.2 Definition for proper spaces using rays
00:26:51 3.3 Examples
00:28:31 3.4 Busemann functions
00:30:43 3.5 The action of isometries on the boundary and their classification
00:31:09 4 More examples
00:34:01 5 See also
00:34:58 6 Notes



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SUMMARY
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In mathematics, a hyperbolic metric space is a metric space satisfying certain metric relations (depending quantitatively on a nonnegative real number δ) between points. The definition, introduced by Mikhael Gromov, generalizes the metric properties of classical hyperbolic geometry and of trees. Hyperbolicity is a large-scale property, and is very useful to the study of certain infinite groups called (Gromov-)hyperbolic groups.