Geodesic currents and counting problems

DOI10.1007/s00039-019-00502-7zbMath1420.30012arXiv1709.06834OpenAlexW2962788967WikidataQ127781574 ScholiaQ127781574MaRDI QIDQ1999362

Kasra Rafi, Juan Souto

Publication date: 26 June 2019

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.06834

zbMATH Keywords

Teichmüller spacecompact Riemann surfacecurrent

Mathematics Subject Classification ID

Compact Riemann surfaces and uniformization (30F10) Teichmüller theory for Riemann surfaces (30F60)

Related Items (12)

Large genus asymptotic geometry of random square-tiled surfaces and of random multicurves ⋮ Counting hyperbolic multigeodesics with respect to the lengths of individual components and asymptotics of Weil-Petersson volumes ⋮ Experimental Statistics for Mirzakhani’s Theorem ⋮ Effective mapping class group dynamics. I: Counting lattice points in Teichmüller space ⋮ Valuations on the character variety: Newton polytopes and residual Poisson bracket ⋮ Counting curves on orbifolds ⋮ Enumerative geometry of surfaces. Abstracts from the workshop held June 13--19, 2021 (hybrid meeting) ⋮ A tour through Mirzakhani’s work on moduli spaces of Riemann surfaces ⋮ Counting square-tiled surfaces with prescribed real and imaginary foliations and connections to Mirzakhani's asymptotics for simple closed hyperbolic geodesics ⋮ Length Functions on Currents and Applications to Dynamics and Counting ⋮ Ergodic invariant measures on the space of geodesic currents ⋮ From curves to currents

Cites Work

• Counting curves in hyperbolic surfaces
• Lattice point asymptotics and volume growth on Teichmüller space
• Invariant Radon measures on measured lamination space
• The geometry of Teichmüller space via geodesic currents
• Bouts des variétés hyperboliques de dimension 3. (Ends of hyperbolic 3-dimensional manifolds)
• On Thurston's boundary of Teichmüller space and the extension of earthquakes
• The Weil-Petersson and Thurston symplectic forms
• Counting curves, and the stable length of currents
• On normalizations of Thurston measure on the space of measured laminations
• Hyperbolic Structures on Surfaces and Geodesic Currents
• Ergodic Theory of the Space of Measured Laminations
• Ergodic Actions of the Mapping Class Group
• Combinatorics of Train Tracks. (AM-125)
• The Weil-Petersson Symplectic Structure at Thurston's Boundary
• Counting One-Sided Simple Closed Geodesics on Fuchsian Thrice Punctured Projective Planes
• Shearing coordinates and convexity of length functions on Teichmüller space
• Counting curves on orbifolds

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