Geometry and Dynamics in Gromov Hyperbolic Metric Spaces

With an Emphasis on Non-Proper Settings

AvTushar Das,David Simmons

Inbunden, Engelska, 2017

Del i serien Mathematical Surveys and Monographs

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Beskrivning

This 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.

Produktinformation

Utgivningsdatum:2017-06-30
Mått:178 x 254 x undefined mm
Vikt:740 g
Format:Inbunden
Språk:Engelska
Serie:Mathematical Surveys and Monographs
Antal sidor:281
Förlag:American Mathematical Society
ISBN:9781470434656

Utforska kategorier

Matematik inom Naturvetenskap och teknik
Algebra inom Naturvetenskap och teknik

Mer om författaren

Tushar Das, University of Wisconsin, La Crosse, WI.David Simmons, University of York, United Kingdom.Mariusz Urbanski, University of North Texas, Denton, TX.

Innehållsförteckning

Preliminaries: Algebraic hyperbolic spaces$\mathbb{R}$-trees, CAT(-1) spaces, and Gromov hyperbolic metric spacesMore about the geometry of hyperbolic metric spacesDiscretenessClassification of isometries and semigroupsLimit setsThe Bishop-Jones theorem: The modified Poincare exponentGeneralization of the Bishop-Jones theoremExamples: Schottky productsParabolic groupsGeometrically finite and convex-cobounded groupsCounterexamples$\mathbb{R}$-trees and their isometry groupsPatterson-Sullivan theory: Conformal and quasiconformal measuresPatterson-Sullivan theorem for groups of divergence typeQuasiconformal measures of geometrically finite groupsOpen problemsIndex of defined termsBibliography