The exponent of convergence of Kleinian groups; on a theorem of Bishop and Jones. Fractal Geometry and Stochastics III, 93-107

Bernd O Stratmann

The exponent of convergence of Kleinian groups; on a theorem of Bishop and Jones. Fractal Geometry and Stochastics III, 93-107

Bernd O Stratmann

Pure Mathematics

Research output: Other contribution

Abstract

In this note we give a characterization of the Hausdorff dimensional significance of the exponent of convergence for any arbitrary Kleinian group. We show that this exponent is always equal to the Hausdorff dimension of the uniformly radial limit sets of the Kleinian group. We give a detailed and elementary proof of this important fact, clarifying and generalizing a result of Bishop and Jones.

Original language	English
Volume	57
Publication status	Published - 2004

Keywords

Kleinian groups
exponent of convergence
fractal geometry
DIOPHANTINE APPROXIMATION
HAUSDORFF DIMENSION
BOUNDED GEODESICS
ISOMETRIES
MANIFOLDS
SPACES

Cite this

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title = "The exponent of convergence of Kleinian groups; on a theorem of Bishop and Jones. Fractal Geometry and Stochastics III, 93-107",

abstract = "In this note we give a characterization of the Hausdorff dimensional significance of the exponent of convergence for any arbitrary Kleinian group. We show that this exponent is always equal to the Hausdorff dimension of the uniformly radial limit sets of the Kleinian group. We give a detailed and elementary proof of this important fact, clarifying and generalizing a result of Bishop and Jones.",

keywords = "Kleinian groups, exponent of convergence, fractal geometry, DIOPHANTINE APPROXIMATION, HAUSDORFF DIMENSION, BOUNDED GEODESICS, ISOMETRIES, MANIFOLDS, SPACES",

author = "Stratmann, {Bernd O}",

note = "Progr Probab",

year = "2004",

language = "English",

isbn = "0817652639",

volume = "57",

type = "Other",

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TY - GEN

T1 - The exponent of convergence of Kleinian groups; on a theorem of Bishop and Jones. Fractal Geometry and Stochastics III, 93-107

AU - Stratmann, Bernd O

N1 - Progr Probab

PY - 2004

Y1 - 2004

N2 - In this note we give a characterization of the Hausdorff dimensional significance of the exponent of convergence for any arbitrary Kleinian group. We show that this exponent is always equal to the Hausdorff dimension of the uniformly radial limit sets of the Kleinian group. We give a detailed and elementary proof of this important fact, clarifying and generalizing a result of Bishop and Jones.

AB - In this note we give a characterization of the Hausdorff dimensional significance of the exponent of convergence for any arbitrary Kleinian group. We show that this exponent is always equal to the Hausdorff dimension of the uniformly radial limit sets of the Kleinian group. We give a detailed and elementary proof of this important fact, clarifying and generalizing a result of Bishop and Jones.

KW - Kleinian groups

KW - exponent of convergence

KW - fractal geometry

KW - DIOPHANTINE APPROXIMATION

KW - HAUSDORFF DIMENSION

KW - BOUNDED GEODESICS

KW - ISOMETRIES

KW - MANIFOLDS

KW - SPACES

M3 - Other contribution

SN - 0817652639

VL - 57

ER -

The exponent of convergence of Kleinian groups; on a theorem of Bishop and Jones. Fractal Geometry and Stochastics III, 93-107

Abstract

Keywords

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