Coarse extrinsic geometry: a survey

Mitra, Mahan (1998) Coarse extrinsic geometry: a survey Geometry & Topology Monographs, 1 . pp. 341-364. ISSN 1464-8997

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This paper is a survey of some of the developments in coarse extrinsic geometry since its inception in the work of Gromov. Distortion, as measured by comparing the diameter of balls relative to different metrics, can be regarded as one of the simplist extrinsic notions. Results and examples concerning distorted subgroups, especially in the context of hyperbolic groups and symmetric spaces, are exposed. Other topics considered are quasiconvexity of subgroups; behaviour at infinity, or more precisely continuous extensions of embedding maps to Gromov boundaries in the context of hyperbolic groups acting by isometries on hyperbolic metric spaces; and distortion as measured using various other filling invariants.

Item Type:Article
Source:Copyright of this article belongs to Geometry and Topology Publications.
Keywords:Coarse Geometry; Quasi-isometry; Hyperbolic Groups
ID Code:89546
Deposited On:28 Apr 2012 12:55
Last Modified:19 May 2016 04:04

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