Geometry & Topology Monographs 1 (1998), The Epstein Birthday Schrift, paper no. 17, pages 341-364.

Coarse extrinsic geometry: a survey

Mahan Mitra

Abstract. 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.

Keywords. Coarse geometry, quasi-isometry, hyperbolic groupsx

AMS subject classification. Primary: 20F32. Secondary: 57M50.

E-print: arXiv:math.DG/9810203

Submitted: 20 November 1997. Published: 30 October 1998.

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Mahan Mitra
Institute of Mathematical Sciences, C.I.T. Campus
Madras (Chennai) -- 600113, India

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