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

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Mathematical Surveys and Monographs ; v.218Publisher: Providence : American Mathematical Society, 2016Description: 1 Online-Ressource (321 p)Subject(s): Additional physical formats: 9781470434656 | 1470440482. | 9781470440480. | Erscheint auch als: Geometry and dynamics in Gromov hyperbolic metric spaces. Druck-Ausgabe Providence, Rhode Island : American Mathematical Society, 2017. xxxv, 281 Seiten | Print version: Geometry and Dynamics in Gromov Hyperbolic Metric Spaces : With an Emphasis on Non-Proper Settings. Providence : American Mathematical Society,c2016DDC classification:
  • 516.362
RVK: RVK: SK 260 | SK 350LOC classification:
  • QA685.D238 2016
Online resources: Summary: 1.4.1. Quasiconformal measures of geometrically finite groups1.5. Appendices; Part 1 . Preliminaries; Chapter 2. Algebraic hyperbolic spaces; 2.1. The definition; 2.2. The hyperboloid model; 2.3. Isometries of algebraic hyperbolic spaces; 2.4. Totally geodesic subsets of algebraic hyperbolic spaces; 2.5. Other models of hyperbolic geometry; 2.5.1. The (Klein) ball model; 2.5.2. The half-space model; 2.5.3. Transitivity of the action of \Isom() on ∂˝; Chapter 3. \R-trees, CAT(-1) spaces, and Gromov hyperbolic metric spaces; 3.1. Graphs and \R-trees; 3.2. CAT(-1) spacesSummary: 3.6.4. The visual metametric based at a point ∈\del Chapter 4. More about the geometry of hyperbolic metric spaces; 4.1. Gromov triples; 4.2. Derivatives; 4.2.1. Derivatives of metametrics; 4.2.2. Derivatives of maps; 4.2.3. The dynamical derivative; 4.3. The Rips condition; 4.4. Geodesics in CAT(-1) spaces; 4.5. The geometry of shadows; 4.5.1. Shadows in regularly geodesic hyperbolic metric spaces; 4.5.2. Shadows in hyperbolic metric spaces; 4.6. Generalized polar coordinates; Chapter 5. Discreteness; 5.1. Topologies on \Isom( ); 5.2. Discrete groups of isometriesSummary: 5.2.1. Topological discreteness5.2.2. Equivalence in finite dimensions; 5.2.3. Proper discontinuity; 5.2.4. Behavior with respect to restrictions; 5.2.5. Countability of discrete groups; Chapter 6. Classification of isometries and semigroups; 6.1. Classification of isometries; 6.1.1. More on loxodromic isometries; 6.1.2. The story for real hyperbolic spaces; 6.2. Classification of semigroups; 6.2.1. Elliptic semigroups; 6.2.2. Parabolic semigroups; 6.2.3. Loxodromic semigroups; 6.3. Proof of the Classification Theorem; 6.4. Discreteness and focal groups; Chapter 7. Limit setsSummary: Cover; Title page; Dedication; Contents; List of Figures; Prologue; Chapter 1. Introduction and Overview; 1.1. Preliminaries; 1.1.1. Algebraic hyperbolic spaces; 1.1.2. Gromov hyperbolic metric spaces; 1.1.3. Discreteness; 1.1.4. The classification of semigroups; 1.1.5. Limit sets; 1.2. The Bishop-Jones theorem and its generalization; 1.2.1. The modified Poincaré exponent; 1.3. Examples; 1.3.1. Schottky products; 1.3.2. Parabolic groups; 1.3.3. Geometrically finite and convex-cobounded groups; 1.3.4. Counterexamples; 1.3.5. \R-trees and their isometry groups; 1.4. Patterson-Sullivan theoryPPN: PPN: 1014136210Package identifier: Produktsigel: ZDB-4-NLEBK
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