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Coarse extrinsic geometry: a survey

Mahan Mitra

Geometry & Topology Monographs 1 (1998) 341–364

DOI: 10.2140/gtm.1998.1.341

arXiv: math.DG/9810203


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.

To David Epstein on his sixtieth birthday.


coarse geometry, quasi-isometry, hyperbolic groupsx

Mathematical Subject Classification

Primary: 20F32

Secondary: 57M50


Received: 20 November 1997
Published: 30 October 1998

Mahan Mitra
Institute of Mathematical Sciences
CIT Campus
Madras (Chennai) – 600113