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OverviewThis book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the geometry of their limit sets and on behavior not found in the proper setting. The authors provide a number of examples of groups which exhibit a wide range of phenomena not to be found in the finite-dimensional theory. The book contains both introductory material to help beginners as well as new research results, and closes with a list of attractive unsolved problems. Full Product DetailsAuthor: Tushar Das , David Simmons , Mariusz UrbanskiPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.740kg ISBN: 9781470434656ISBN 10: 1470434652 Pages: 281 Publication Date: 30 June 2017 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsPreliminaries: Algebraic hyperbolic spaces $\mathbb{R}$-trees, CAT(-1) spaces, and Gromov hyperbolic metric spaces More about the geometry of hyperbolic metric spaces Discreteness Classification of isometries and semigroups Limit sets The Bishop-Jones theorem: The modified Poincare exponent Generalization of the Bishop-Jones theorem Examples: Schottky products Parabolic groups Geometrically finite and convex-cobounded groups Counterexamples $\mathbb{R}$-trees and their isometry groups Patterson-Sullivan theory: Conformal and quasiconformal measures Patterson-Sullivan theorem for groups of divergence type Quasiconformal measures of geometrically finite groups Open problems Index of defined terms BibliographyReviewsAuthor InformationTushar Das, University of Wisconsin, La Crosse, WI. David Simmons, University of York, United Kingdom. Mariusz Urbanski, University of North Texas, Denton, TX. Tab Content 6Author Website:Countries AvailableAll regions |
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