The Poincaré metric and a conformal version of a theorem of Thurston

DOI10.1215/S0012-7094-91-06417-3zbMath0759.57013MaRDI QIDQ1190842

Richard D. Canary

Publication date: 27 September 1992

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

hyperbolic manifoldKleinian groupsPoincaré metricdomain of discontinuityBers slice theoremquasi-conformal deformationThurston's compactness theorem

Mathematics Subject Classification ID

Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) General geometric structures on low-dimensional manifolds (57M50) Discontinuous groups of transformations (57S30) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40)

Related Items (14)

Algebraic Convergence of Schottky Groups ⋮ Intersections of topologically tame subgroups of Kleinian groups ⋮ Wiggly sets and limit sets ⋮ Hausdorff dimension and Kleinian groups ⋮ Algebraic and geometrix convergence of discrete representations into PSL\(_2\mathbb C\) ⋮ The Thurston metric on hyperbolic domains and boundaries of convex hulls ⋮ Non-realizability and ending laminations: proof of the density conjecture ⋮ Uniform perfectness of the limit sets of Kleinian groups ⋮ Realising end invariants by limits of minimally parabolic, geometrically finite groups ⋮ Intersections of Analytically and Geometrically Finite Subgroups of Kleinian Groups ⋮ The Double Limit Theorem and Its Legacy ⋮ Constructing geometrically infinite groups on boundaries of deformation spaces ⋮ The conformal boundary and the boundary of the convex core ⋮ A note on geometric upper bounds for the exponent of convergence of convex cocompact Kleinian groups

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• Algebraic Convergence of Schottky Groups
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