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.
Notes on file formats
Mahan Mitra
Institute of Mathematical Sciences, C.I.T. Campus
Madras (Chennai) -- 600113, India
Email: mitra@imsc.ernet.in
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