On quasiconformal groups

DOI10.1007/BF02796595zbMath0603.30026MaRDI QIDQ1082479

Pekka Tukia

Publication date: 1986

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

zbMATH Keywords

conformal structureK-quasiconformal homeomorphism

Mathematics Subject Classification ID

Quasiconformal mappings in the complex plane (30C62)

Related Items (32)

Quasiregular mappings on sub-Riemannian manifolds ⋮ Rigidity for convex-cocompact actions on rank-one symmetric spaces ⋮ Large scale geometry of certain solvable groups. ⋮ Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary. ⋮ On the logarithmic coarse structures of Lie groups and hyperbolic spaces ⋮ Some topological characterizations of rational maps and Kleinian groups ⋮ Bilipschitz equivalence is not equivalent to quasi-isometric equivalence for finitely generated groups. ⋮ Quasiconformality in the geodesic flow of negatively curved manifolds ⋮ Hyperbolic convexes and quasiisometries. ⋮ Cocycles with one exponent over partially hyperbolic systems ⋮ A fibered Tukia theorem for nilpotent Lie groups ⋮ Flows, fixed points and rigidity for Kleinian groups ⋮ A note on laminations with symmetric leaves ⋮ Coarse \(\mathcal{Z}\)-boundaries for groups ⋮ On classification of higher rank Anosov actions on compact manifold ⋮ Groups quasi-isometric to right-angled Artin groups ⋮ Uniformly quasiregular mappings of Lattès type ⋮ Recognizing constant curvature discrete groups in dimension 3 ⋮ Rigidity in holomorphic and quasiregular dynamics ⋮ Metric conformal structures and hyperbolic dimension ⋮ Quasiconformal groups with small dilatation II ⋮ Structure of partially hyperbolic Hénon maps ⋮ Induced quasi-actions: A remark ⋮ Quasi‐isometric groups with no common model geometry ⋮ Quasi‐Mobius Homeomorphisms of Morse boundaries ⋮ Conformally formal manifolds and the uniformly quasiregular non-ellipticity of \((\mathbb{S}^2 \times\mathbb{S}^2)\#(\mathbb{S}^2\times\mathbb{S}^2)\) ⋮ Lattice envelopes ⋮ Anti-de Sitter strictly GHC-regular groups which are not lattices ⋮ Quasiregular analogues of critically finite rational functions with parabolic orbifold ⋮ On the asymptotic geometry of Abelian-by-cyclic groups ⋮ Differentiability and rigidity of Möbius groups ⋮ Quasiconformal groups, Patterson-Sullivan theory, and local analysis of limit sets

Cites Work

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• The boundary correspondence under quasiconformal mappings
• Differentiability and rigidity of Möbius groups
• Extremal length definitions for the conformal capacity of rings in space
• Quasiconformally homogeneous domains
• Quasiconformal extension of quasisymmetric mappings compatible with a Möbius group
• Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms
• Lectures on \(n\)-dimensional quasiconformal mappings
• Siegel's modular forms and Dirichlet series. Course given at the University of Maryland, 1969-1970
• The L\(^p\)-integrability of the partial derivatives of a quasiconformal mapping
• A remark on 1-quasiconformal maps
• Uniformly Quasisymmetric Groups
• Discrete quasiconformal groups that are not the quasiconformal conjugates of Möbius groups
• A quasiconformal group not isomorphic to a Möbius group
• On two-dimensional quasiconformal groups

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