Hyperbolic Structures for Surfaces of Infinite Type

DOI10.2307/2154353zbMath0768.30028OpenAlexW4248780597MaRDI QIDQ4038458

Ara Basmajian

Publication date: 16 May 1993

Full work available at URL: https://doi.org/10.2307/2154353

zbMATH Keywords

geodesichyperbolic surfacespair of pants

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

Related Items (22)

The heights theorem for infinite Riemann surfaces ⋮ Train tracks and measured laminations on infinite surfaces ⋮ Parabolicity of zero-twist tight flute surfaces and uniformization of the Loch Ness monster ⋮ Large parameter spaces of quasiconformally distinct hyperbolic structures ⋮ Gromov hyperbolicity of Denjoy domains ⋮ Ideally, all infinite‐type surfaces can be triangulated ⋮ The type problem for Riemann surfaces via Fenchel–Nielsen parameters ⋮ Ergodicity of the geodesic flow on symmetric surfaces ⋮ Flip graphs for infinite type surfaces ⋮ The arc metric on Teichmüller spaces of surfaces of infinite type with boundary ⋮ Inequivalent topologies on the Teichmüller space of the flute surface ⋮ Thurston’s boundary for Teichmüller spaces of infinite surfaces: the length spectrum ⋮ Pants decomposition and intersections of closed geodesics on geometrically infinite hyperbolic surfaces ⋮ Some metrics on Teichmüller spaces of surfaces of infinite type ⋮ The geometry at infinity of a hyperbolic Riemann surface of infinite type ⋮ A real variable characterization of Gromov hyperbolicity of flute surfaces ⋮ Twists and Gromov hyperbolicity of Riemann surfaces ⋮ A countable Teichmüller modular group ⋮ On various Teichmüller spaces of a surface of infinite topological type ⋮ Geodesically Complete Hyperbolic Structures ⋮ Properties of metrics on Teichmüller spaces of surfaces of infinite type ⋮ Planar Riemann surfaces with uniformly distributed cusps: parabolicity and hyperbolicity

Cites Work

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• A cutting and pasting of noncompact polygons with applications to Fuchsian groups
• The real analytic theory of Teichmüller space
• Constructing pairs of pants

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