On isomorphisms of geometrically finite Möbius groups

DOI10.1007/BF02698805zbMath0572.30036MaRDI QIDQ1062176

Pekka Tukia

Publication date: 1985

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=PMIHES_1985__61__171_0

zbMATH Keywords

Mostow's rigidity theoremgeometrically finite Möbius groupstype-preserving isomorphism

Mathematics Subject Classification ID

Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40) Quasiconformal mappings in the complex plane (30C62)

Related Items (35)

Quasiconformal stability of Kleinian groups and an embedding of a space of flat conformal structures ⋮ RELATIVELY HYPERBOLIC GROUPS ⋮ Topological barriers for locally homeomorphic quasiregular mappings in 3-space ⋮ The limit sets of subgroups of lattices in \(\mathrm {PSL}(2,\mathbb R)^r\) ⋮ Hausdorff dimension varies continuously on equivalent dynamically defined wild knots ⋮ Convex-cocompactness of Kleinian groups and conformally flat manifolds with positive scalar curvature ⋮ Quasiregular mappings and discrete group actions ⋮ Fake Schottky groups acting on the 3-sphere ⋮ Exotic actions of free Kleinian groups ⋮ The geometry of Nielsen's hull for a Kleinian group in space and quasi- conformal mappings ⋮ Limit sets of Kleinian groups and conformally flat Riemannian manifolds ⋮ The limit map of a homomorphism of discrete Möbius groups ⋮ A rigidity theorem for Möbius groups ⋮ Some curious Kleinian groups and hyperbolic 5-manifolds ⋮ Limits of limit sets. I ⋮ A WILD KNOT 𝕊²↪ 𝕊⁴AS LIMIT SET OF A KLEINIAN GROUP: INDRA'S PEARLS IN FOUR DIMENSIONS ⋮ Rigidity of Kleinian groups via self-joinings ⋮ Schottky type groups and Kleinian groups acting on S3 with the limit set a wild Cantor set ⋮ Manhattan curves for hyperbolic surfaces with cusps ⋮ On discrete Möbius groups in all dimensions: A generalization of Jørgensen's inequality ⋮ Zeta functions that hear the shape of a Riemann surface ⋮ Group Completions and Orbifolds of Variable Negative Curvature ⋮ A Bowen type rigidity theorem for non-cocompact hyperbolic groups ⋮ Tukia's isomorphism theorem in CAT(–1) spaces ⋮ Hyperbolic manifolds with geodesic boundary which are determined by their fundamental group ⋮ Quasiconformal extension of quasisymmetric mappings compatible with a Möbius group ⋮ Remarques sur le spectre des longueurs d'une surface et comptages ⋮ Commensurability of hyperbolic manifolds with geodesic boundary ⋮ Hyperbolic topology and bounded locally homeomorphic quasiregular mappings in 3-space ⋮ Kleinian groups acting on \(S^3\) which are extensions ⋮ The Hausdorff dimension of the limit set of a geometrically finite Kleinian group ⋮ Differentiability and rigidity of Möbius groups ⋮ Deformation of Schottky groups in complex hyperbolic space ⋮ Conformal dimension and boundaries of planar domains ⋮ Bers slices in families of univalent maps

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