Counting curves in hyperbolic surfaces

DOI10.1007/s00039-016-0374-7zbMath1350.57017arXiv1508.02265OpenAlexW2213694853MaRDI QIDQ311137

Juan Souto, Viveka Erlandsson

Publication date: 29 September 2016

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

Full work available at URL: https://arxiv.org/abs/1508.02265

zbMATH Keywords

hyperbolic surfacenumber of curves hyperbolic surfacenumber of curves of bounded length

Mathematics Subject Classification ID

General geometric structures on low-dimensional manifolds (57M50)

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Cites Work

• Lower bound on the number of non-simple closed geodesics on surfaces
• Length spectra and degeneration of flat metrics
• Geodesics with one self-intersection, and other stories
• Homogeneous asymptotic limits of Haar measures of semisimple linear groups and their lattices
• Le spectre marqué des longueurs des surfaces à courbure négative. (The spectrum marked by lengths of surfaces with negative curvature)
• The geometry of Teichmüller space via geodesic currents
• Measured lamination spaces for surfaces, from the topological viewpoint
• Bouts des variétés hyperboliques de dimension 3. (Ends of hyperbolic 3-dimensional manifolds)
• Growth of the number of simple closed geodesics on hyperbolic surfaces
• Ergodic Actions of the Mapping Class Group
• Combinatorics of Train Tracks. (AM-125)
• Angular self-intersections for closed geodesics on surfaces
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