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Lectures on spaces of nonpositive curvature

Author: Werner Ballmann; Misha Brin
Publisher: Basel ; Boston ; Berlin : Birkhäuser Verlag, cop. 1995.
Series: DMV-Seminar, 25.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology,  Read more...

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Document Type: Book
All Authors / Contributors: Werner Ballmann; Misha Brin
ISBN: 0817652426 9780817652425 3764352426 9783764352424
OCLC Number: 490512924
Description: 1 vol. (V-112 p.) ; 24 cm.
Contents: I. On the interior geometry of metric spaces.- 1. Preliminaries.- 2. The Hopf-Rinow Theorem.- 3. Spaces with curvature bounded from above.- 4. The Hadamard-Cartan Theorem.- 5. Hadamard spaces.- II. The boundary at infinity.- 1. Closure of X via Busemann functions.- 2. Closure of X via rays.- 3. Classification of isometries.- 4. The cone at infinity and the Tits metric.- III. Weak hyperbolicity.- 1. The duality condition.- 2. Geodesic flows on Hadamard spaces.- 3. The flat half plane condition.- 4. Harmonic functions and random walks on ?.- IV. Rank rigidity.- 1. Preliminaries on geodesic flows.- 2. Jacobi fields and curvature.- 3. Busemann functions and horospheres.- 4. Rank, regular vectors and flats.- 5. An invariant set at infinity.- 6. Proof of the rank rigidity.- Appendix. Ergodicity of geodesic flows.- 1. Introductory remarks.- Measure and ergodic theory preliminaries.- Absolutely continuous foliations.- Anosov flows and the Ho continuity of invariant distributions.- Proof of absolute continuity and ergodicity.
Series Title: DMV-Seminar, 25.
Responsibility: Werner Ballmann ; with an appendix by Misha Brin, Ergodicity of geodesic flows.

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