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Geometry and Dynamics in Gromov Hyperbolic Metric Spaces: With an Emphasis on Non-Proper Settings

Tushar Das University of Wisconsin, La Crosse, La Crosse, WI
David Simmons University of York, York, United Kingdom
Mariusz Urbański University of North Texas, Denton, TX
Available Formats:
Hardcover ISBN: 978-1-4704-3465-6
Product Code: SURV/218
List Price: $116.00 MAA Member Price:$104.40
AMS Member Price: $92.80 Electronic ISBN: 978-1-4704-4048-0 Product Code: SURV/218.E List Price:$116.00
MAA Member Price: $104.40 AMS Member Price:$92.80
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List Price: $174.00 MAA Member Price:$156.60
AMS Member Price: $139.20 Click above image for expanded view Geometry and Dynamics in Gromov Hyperbolic Metric Spaces: With an Emphasis on Non-Proper Settings Tushar Das University of Wisconsin, La Crosse, La Crosse, WI David Simmons University of York, York, United Kingdom Mariusz Urbański University of North Texas, Denton, TX Available Formats:  Hardcover ISBN: 978-1-4704-3465-6 Product Code: SURV/218  List Price:$116.00 MAA Member Price: $104.40 AMS Member Price:$92.80
 Electronic ISBN: 978-1-4704-4048-0 Product Code: SURV/218.E
 List Price: $116.00 MAA Member Price:$104.40 AMS Member Price: $92.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$174.00 MAA Member Price: $156.60 AMS Member Price:$139.20
• Book Details

Mathematical Surveys and Monographs
Volume: 2182017; 281 pp
MSC: Primary 20; 28; 37; Secondary 22;

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.

Graduate students and researchers interested in geometric group theory and Gromov-hyperbolic spaces.

• Preliminaries
• 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 Poincaré 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

• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 2182017; 281 pp
MSC: Primary 20; 28; 37; Secondary 22;

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.

Graduate students and researchers interested in geometric group theory and Gromov-hyperbolic spaces.

• Preliminaries
• 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 Poincaré 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
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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