4 edition of **Uniformizing Gromov hyperbolic spaces** found in the catalog.

Uniformizing Gromov hyperbolic spaces

Mario Bonk

- 332 Want to read
- 30 Currently reading

Published
**2001**
by Société mathématique de France in Paris
.

Written in English

- Hyperbolic spaces.

**Edition Notes**

Statement | Mario Bonk, Juha Heinonen, Pekka Koskela. |

Series | Astérisque,, 270 |

Contributions | Heinonen, Juha., Koskela, Pekka. |

Classifications | |
---|---|

LC Classifications | QA685 .B74 2001 |

The Physical Object | |

Pagination | vi, 99 p. ; |

Number of Pages | 99 |

ID Numbers | |

Open Library | OL4018767M |

ISBN 10 | 2856290981 |

LC Control Number | 2001395055 |

OCLC/WorldCa | 47078590 |

to proper Gromov hyperbolic spaces which satisfy the following two additional conditions: (Bounded geometry) Every R-ball can be covered by at most N= N(R;r) balls of radius r R. (Nondegeneracy) There is a C2[0;1) such that every point xlies within distance at most C from all three sides of some ideal geodesic triangle x. In this article we exhibit the largest constant in a quadratic isoperimetric inequality which ensures that a geodesic metric space is Gromov hyperbolic. As a particular consequence we obtain that Euclidean space is a borderline case for Gromov hyperbolicity in terms of the isoperimetric function. We prove similar results for the linear filling radius inequality. Our results strengthen and Cited by:

Abstract: 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 hyperbolic plane is a covering space. Contents 1. Hyperbolic Geometry and PSL(2,R) 1 2. Geodesics 5 3. Discrete Isometry Groups and Proper Discontinuity 8 4. Topological Properties of Fuchsian Groups 12 Acknowledgments 15 References 16 1. Hyperbolic Geometry and PSL(2,R) There are several models of hyperbolic space, but for the purposes of File Size: KB.

hyperbolic space ∗, † Abstract In this article we produce an example of a non-residually ﬁnite group which admits a uniformly proper action on a Gromov hyperbolic space. 1 Introduction By default, all actions of groups on metric spaces considered in this paper are by isometries. Other articles where Hyperbolic space is discussed: Maryam Mirzakhani: In hyperbolic space, in contrast to normal Euclidean space, Euclid’s fifth postulate (that one and only one line parallel to a given line can pass through a fixed point) does not hold. In non-Euclidean hyperbolic space, an infinite number of parallel lines can pass through such.

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ISBN: OCLC Number: Language Note: Text engl. mit franz. Zsfassung. Notes: Literaturverz. [95] - Parallelsacht. : Uniformizing Gromov Hyperbolic Spaces (Astérisque) (): Bonk, Mario, Heinonen, Juha, Koskela, Pekka: Books.

The uniformization and hyperbolization transformations formulated by Bonk, Heinonen and Koskela in \emph{"Uniformizing Gromov Hyperbolic Spaces"}, Ast\'erisque {\bf } (), dealt with.

UNIFORMIZING GROMOV HYPERBOLIC SPACES Mario Bonk, Juha Heinonen, Pekka Koskela Abstract. The unit disk in the complex plane has two conformally related lives: one as an incomplete spac wite h the metric inherited fro2,m th Re othe ars a complete Riemannian 2.

In mathematics, a hyperbolic metric space is a metric space satisfying certain metric relations (depending quantitatively on a nonnegative real number δ) Uniformizing Gromov hyperbolic spaces book points. The definition, introduced by Mikhael Gromov, generalizes the metric properties of classical hyperbolic geometry and of olicity is a large-scale property, and is very useful to the study of certain infinite groups.

Gromov hyperbolic metric spaces by the use of these examples. Note that in the second example, the order of the points in the Cayley distance in (1) is chosen so that the cross-ratio yields a value greater than 1. References [1] M. Bonk, J. Heinonen and P. Koskela, Uniformizing Gromov hyperbolic spaces, Aste´risque, () –File Size: 40KB.

Uniformizing Gromov Hyperbolic Spaces by Mario Bonk,available at Book Depository with free delivery worldwide. 2 MISHA KAPOVICH Then the ideal boundary of a Gromov{hyperbolic group G is deﬂned as @1¡G; where ¡G is a Cayley graph of ¡G is well-deﬂned up to a quasi-symmetric homeomorphism.

Ideal boundaries of CAT(0) er a CAT(0) space geodesic rays ﬁ;ﬂ: R+!X are said to be equivalent if there exists a constant C 2 Rsuch that d(ﬁ(t);ﬂ(t)) • C;8t 2 R+.

Gromov hyperbolic spaces, also known as $\delta$-hyperbolic spaces, are geodesic spaces in which every triangle is thin. Hyperbolic groups are fundamental examples of Gromov hyperbolic spaces in geometric group theory.

spaces with various restrictions. A group G is hyperbolic (or word-hyperbolic or Gromov-hyperbolic) if for some δ it acts geometrically on some δ-hyperbolic space. Similarly, a group G is a CAT(κ) group if it acts geometrically on some CAT(κ) space. Deciding whether a group is File Size: KB. Bonk, Mario; Heinonen, Juha; Koskela, Pekka.

Uniformizing Gromov hyperbolic spaces. Astérisque, no. (), p. Follow Mario Bonk and explore their bibliography from 's Mario Bonk Author Page. Gromov hyperbolic spaces generalize notions such as simplicial trees and Riemannian manifolds with constant negative sectional curvature while preserving most of the interesing properties [6, 18 Author: Jussi Väisälä.

The theory of Gromov hyperbolic spaces, introduced by M. Gromov in the eighties, has been considered in the books [CDP], [GdH], [Sh], [Bow], [BH], [BBI], [Ro] and in several papers, but it is often assumed that the spaces are geodesic and usually also proper (closed bounded sets are compact).

It is shown that a Gromov hyperbolic geodesic metric space X with bounded growth at some scale is roughly quasi-isometric to a convex subset of hyperbolic space.

If one is allowed to rescale the metric of X by some positive constant, then there is an embedding where distances are distorted by at most an additive constant.Another embedding theorem states that any $ \delta $ -hyperbolic metric Cited by: Harmonic quasi-isometric maps between rank one symmetric spaces We prove that a quasi-isometric map between rank one symmetric spaces is within bounded distance from a unique harmonic map.

In particular, this completes the proof of the Schoen-Li-Wang conjecture. Bonk, J. Heinonen, and P. Koskela, Uniformizing Gromov Hyperbolic Spaces Cited by: 4. Browse other questions tagged group-theory geometric-group-theory open-problem gromov-hyperbolic-spaces or ask your own question.

Featured on Meta Creative Commons Licensing UI and Data Updates. Abstract. The goal of this chapter is to explain some connections between hyperbolicity in the sense of Gromov and complex analysis/geometry. For this, we first give a short presentation of the theory of Gromov hyperbolic spaces and their by: 1.

hyperbolic space in the sense of Gromov. This notion provides a uniform "global" approach to such objects as the hyperbolic plane, simply-connected Riemannian manifolds with pinched negative sectional curvature, -spaces, and metric s "hyperbolic properties" introduced earlier (mostly in the context of group theory), were summed up and further developed by M.

Gromov in his. The Mathematical Sciences Research Institute (MSRI), founded inis an independent nonprofit mathematical research institution whose funding sources include the National Science Foundation, foundations, corporations, and more than 90 universities and institutions.

The Institute is located at 17 Gauss Way, on the University of California, Berkeley campus, close to Grizzly Peak, on the.2. Hyperbolic spaces. Summary. I start each section with a brief summary. In Section 2, we give the definition and the basic properties of hyperbolic spaces. The definition is given in terms of the Gromov product.

An alternative characterization for intrinsic hyperbolic spaces in terms of slim triangles is also given. Notation and Cited by: CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. In this article we exhibit the largest constant in a quadratic isoperimetric inequality which ensures that a geodesic metric space is Gromov hyperbolic.

As a particular consequence we obtain that Euclidean space is a borderline case for Gromov hyperbolicity in terms of the isoperimetric function.