Asymptotics of Weil-Petersson geodesics. I: Ending laminations, recurrence, and flows

DOI10.1007/s00039-009-0034-2zbMath1216.32007arXiv0802.1370OpenAlexW2592655192WikidataQ56873224 ScholiaQ56873224MaRDI QIDQ2269892

Yair N. Minsky, Jeffrey F. Brock, Howard A. Masur

Publication date: 12 March 2010

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

Full work available at URL: https://arxiv.org/abs/0802.1370

zbMATH Keywords

ending laminationWeil-Petersson geodesic flowasymptotics of geodesics in the Weil-Petersson metric on the Teichmüller spaceGromov-boundary

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Non-Euclidean differential geometry (53A35) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (20)

Injections of mapping class groups ⋮ Prescribing the behavior of Weil–Petersson geodesics in the moduli space of Riemann surfaces ⋮ Topological dynamics of the Weil-Petersson geodesic flow ⋮ Curve Complexes Versus Tits Buildings: Structures and Applications ⋮ Bottlenecks for Weil-Petersson geodesics ⋮ Growth of the Weil-Petersson inradius of moduli space ⋮ The asymptotic cone of Teichmüller space and thickness ⋮ The Weil-Petersson geodesic flow is ergodic ⋮ The genus of curve, pants and flip graphs ⋮ Geometry of the Funk metric on Weil-Petersson spaces ⋮ The convex core of quasifuchsian manifolds with particles ⋮ Convex hull of set in thick part of Teichmüller space ⋮ Uniform hyperbolicity of the curve graph via surgery sequences ⋮ Contracting boundaries of CAT(0) spaces ⋮ Asymptotics of Weil-Petersson geodesics. II: Bounded geometry and unbounded entropy ⋮ Limit sets of Teichmüller geodesics with minimal nonuniquely ergodic vertical foliation. II ⋮ Rates of mixing for the Weil-Petersson geodesic flow. I: No rapid mixing in non-exceptional moduli spaces ⋮ Coarse and synthetic Weil-Petersson geometry: Quasi-flats, geodesics and relative hyperbolicity ⋮ Limit sets of Weil–Petersson geodesics with nonminimal ending laminations ⋮ Weil-Petersson geodesics on the modular surface

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