Circle packings and co-compact extensions of Kleinian groups

DOI10.1007/BF01389263zbMath0578.30037OpenAlexW2009742684MaRDI QIDQ1066310

Robert Brooks

Publication date: 1986

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143402

zbMATH Keywords

Schottky groupsquasi-conformal deformationscircle packings of Riemann surfacescontinued fraction coordinates

Mathematics Subject Classification ID

Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40)

Related Items (14)

A circle packing algorithm ⋮ Totally geodesic boundaries of knot complements ⋮ Effective drilling and filling of tame hyperbolic 3-manifolds ⋮ The set of circle packing points in the Teichmüller space of a surface of finite conformal type is dense ⋮ On superintegral Kleinian sphere packings, bugs, and arithmetic groups ⋮ Constructing knots with specified geometric limits ⋮ Three techniques for obtaining algebraic circle packings ⋮ Thick-skinned 3-manifolds ⋮ Circle packings and polyhedral surfaces ⋮ Circle packing coordinates for the moduli space of tori ⋮ Heegaard genus and property τ for hyperbolic 3-manifolds ⋮ Hyperbolic groups with planar boundaries ⋮ Constructing quasiconformal maps using circle packings and Brooks's parameterization of quadrilaterals ⋮ All flat three-manifolds appear as cusps of hyperbolic four-manifolds

Cites Work

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• On the deformation theory of classical Schottky groups
• Quasiconformal homeomorphisms and dynamics. II: Structural stability implies hyperbolicity for Kleinian groups
• The geometry of finitely generated Kleinian groups
• Three dimensional manifolds, Kleinian groups and hyperbolic geometry
• Finitely Generated Kleinian Groups

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