Uniform perfectness of the limit sets of Kleinian groups

DOI10.1090/S0002-9947-01-02775-1zbMath0967.30024OpenAlexW1926709621MaRDI QIDQ2716152

Toshiyuki Sugawa

Publication date: 6 June 2001

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-01-02775-1

zbMATH Keywords

Hausdorff dimensionKleinian grouptranslation lengthnniform perfectness

Mathematics Subject Classification ID

Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40)

Related Items (8)

Stability and measurability of the modified lower dimension ⋮ On the hyperbolic distance of \(n\)-times punctured spheres ⋮ Realising end invariants by limits of minimally parabolic, geometrically finite groups ⋮ A conformally invariant metric on Riemann surfaces associated with integrable holomorphic quadratic differentials ⋮ The Double Limit Theorem and Its Legacy ⋮ Regularity of Kleinian limit sets and Patterson-Sullivan measures ⋮ The conformal boundary and the boundary of the convex core ⋮ No ensemble averaging below the black hole threshold

Cites Work

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• Iteration on Teichmüller space
• The Poincaré metric and a conformal version of a theorem of Thurston
• Characterization of Fuchsian groups whose integrable forms are bounded
• Uniformly perfect sets and the Poincaré metric
• Hausdorff dimension and Kleinian groups
• Systoles and topological Morse functions for Riemann surfaces.
• On boundaries of Teichmüller spaces and on Kleinian groups. I
• On the capacity of general Cantor sets
• On limit sets of geometrically finite Kleinian groups.
• Comparison of hyperbolic and extremal lengths
• Various domain constants related to uniform perfectness
• ON UNIFORMLY PERFECT SETS AND FUCHSIAN CROUPS
• The Poincaré Metric of Plane Domains
• Frontiers in complex dynamics
• Uniformly Perfect Sets and Quasiregular Mappings
• Uniformly perfect sets, rational semigroups, Kleinian groups and IFS’s

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