Hausdorff dimension and Kleinian groups

DOI10.1007/BF02392718zbMath0921.30032arXivmath/9403222OpenAlexW1986051960MaRDI QIDQ1384833

Christopher J. Bishop, Peter W. Jones

Publication date: 15 September 1999

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9403222

zbMATH Keywords

limit set Hausdorff dimension Kleinian groups conical limit point Poincaré exponent geometrically finite group

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Teichmüller theory for Riemann surfaces (30F60) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40) Hausdorff and packing measures (28A78)

Related Items

Discrete subgroups of small critical exponent, On horospheric limit sets of Kleinian groups, Continuity of critical exponent of quasiconvex-cocompact groups under Gromov–Hausdorff convergence, Patterson–Sullivan theory for Anosov subgroups, Effective equidistribution of circles in the limit sets of Kleinian groups, A transcendental Julia set of dimension 1, Cheeger isoperimetric constant of Gromov hyperbolic manifolds and graphs, Hausdorff dimension varies continuously on equivalent dynamically defined wild knots, Convex-cocompactness of Kleinian groups and conformally flat manifolds with positive scalar curvature, Bounded orbits of Anosov flows, Orbital functions and heat kernels of Kleinian groups, Phase transitions in 3D gravity and fractal dimension, Fractal models for normal subgroups of Schottky groups, Conformal fractals for normal subgroups of free groups, On the critical exponent of a discrete group of hyperbolic isometries, The Poincaré Exponent and the Dimensions of Kleinian Limit Sets, On quasiconformal invariance of convergence and divergence types for Fuchsian groups, Limit points badly approximable by horoballs, Fractal Weyl laws for asymptotically hyperbolic manifolds, The Apollonian structure of Bianchi groups, On the critical exponent of infinitely generated Veech groups, Conditions for Infinitely Generated Kleinian Groups with Small Limit Sets, Jarník-type inequalities, Wiggly sets and limit sets, Classical Schottky groups of real type of genus two. III, Sequences of porous sets and an application to Kleinian Groups, Hausdorff dimension of limit sets, On the Hausdorff dimension distortions of quasi-symmetric homeomorphisms, Critical exponents of invariant random subgroups in negative curvature, Dimensions of Kleinian orbital sets, A new perspective on the Sullivan dictionary via Assouad type dimensions and spectra, Hitchin representations of Fuchsian groups, Two applications of the natural map, The Martin boundary of an extension by a hyperbolic group, Parabolicity on graphs, Trace theorem for quasi-Fuchsian groups, Geodesics on quotient manifolds and their corresponding limit points, Pattern rigidity and the Hilbert-Smith conjecture., Hausdorff dimension of non-conical limit sets, Local-global principles in circle packings, Differential box counting methods for estimating fractal dimension of gray-scale images: a survey, On hyperbolic once-punctured-torus bundles. IV: Automata for lightning curves, Quasiconformal Lipschitz maps, Sullivan's convex hull theorem and Brennan's conjecture, Escaping geodesics in Riemannian surfaces with variable negative curvature, Uniform perfectness of the limit sets of Kleinian groups, An explicit construction of Kleinian groups with small limit sets, Checking atomicity of conformal ending measures for Kleinian groups, On optimal 4-dimensional metrics, The geometric traveling salesman problem in the Heisenberg group, Dimension rigidity in conformal structures, Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces, ON BADLY APPROXIMABLE COMPLEX NUMBERS, Counting closed geodesics in globally hyperbolic maximal compact AdS 3-manifolds, Large and small covers of a hyperbolic manifold, The structure of two-parabolic space: parabolic dust and iteration, Limit set intersection theorems for Kleinian groups and a conjecture of Susskind, Swiss cheese, dendrites, and quasiconformal homogeneity, A Bowen type rigidity theorem for non-cocompact hyperbolic groups, A lower bound for the exponent of convergence of normal subgroups of Kleinian groups, Hausdorff dimension and dendritic limit sets, Variational principle and Kleinian groups, Remarks on Hausdorff dimensions for transient limits sets of Kleinian groups, Diophantine approximation and badly approximable sets, Rigidity and \(L^2\) cohomology of hyperbolic manifolds, Isoperimetric inequalities in Riemann surfaces and graphs, Hausdorff dimension and conformal measures of Feigenbaum Julia sets, A remark on densities of hyperbolic dimensions for conformal iterated function systems with applications to conformal dynamics and fractal number theory, Constructing restricted Patterson measures for geometrically infinite Kleinian groups, Escaping geodesics of Riemannian surfaces, A multifractal analysis for cuspidal windings on hyperbolic surfaces, Non-uniform hyperbolicity in complex dynamics, Constructing equivariant maps for representations, A note on isoperimetric inequalities of Gromov hyperbolic manifolds and graphs, Measures and dimensions in conformal dynamics, Compact deformations of Fuchsian groups, All finitely generated Kleinian groups of small Hausdorff dimension are classical Schottky groups, Regularity of Kleinian limit sets and Patterson-Sullivan measures, Hausdorff dimension of boundaries of relatively hyperbolic groups, A vanishing theorem for the homology of discrete subgroups of Sp( n , 1) and F ₄ ^–20, Dimensions of limit sets of Kleinian groups, Lebesgue measure of Feigenbaum Julia sets, Metrical Diophantine approximation for quaternions, Pressure, Poincaré series and box dimension of the boundary, The Assouad spectrum of Kleinian limit sets and patterson-Sullivan measure, Boundary conformal field theories, limit sets of Kleinian groups and holography, Geometric branched covers between generalized manifolds, Quasiconformal groups and a theorem of Bishop and Jones, Spectral theory, Hausdorff dimension and the topology of hyperbolic 3-manifolds, Cheeger constants and \(L^2\)-Betti numbers, Quasi-isometries and isoperimetric inequalities in planar domains, Limit sets of discrete groups of isometries of exotic hyperbolic spaces, On Ruelle’s property, Conical limit set and Poincaré exponent for iterations of rational functions, The critical exponent, the Hausdorff dimension of the limit set and the convex core entropy of a Kleinian group, Geometry of Kleinian groups and its applications, A note on geometric upper bounds for the exponent of convergence of convex cocompact Kleinian groups, On the Hausdorff dimension of the Gieseking fractal, Thermodynamic formalism for transient dynamics on the real line, On the Patterson-Sullivan measure of some discrete group of isometries, Quasiconformal groups, Patterson-Sullivan theory, and local analysis of limit sets

Cites Work