Weil-Petersson geodesics on the modular surface

DOI10.1007/s00209-022-03171-9OpenAlexW3107178352WikidataQ126077058 ScholiaQ126077058MaRDI QIDQ2108992

Vaibhav Gadre

Publication date: 20 December 2022

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.12034

zbMATH Keywords

Teichmüller theorymoduli of Riemann surfaces

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Teichmüller theory for Riemann surfaces (30F60) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Cites Work

• Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow
• The Weil-Petersson geodesic flow is ergodic
• Rates of mixing for the Weil-Petersson geodesic flow: exponential mixing in exceptional moduli spaces
• Geodesic-length functions and the Weil-Petersson curvature tensor
• Rates of mixing for the Weil-Petersson geodesic flow. I: No rapid mixing in non-exceptional moduli spaces
• Ergodicity of the geodesic flow on non-complete negatively curved surfaces
• Topological dynamics of the Weil-Petersson geodesic flow
• Recurrent Weil-Petersson geodesic rays with non-uniquely ergodic ending laminations
• Behavior of geodesic-length functions on Teichmüller space
• Hausdorff dimension of the set of nonergodic foliations of a quadratic differential
• Cusp excursions of random geodesics in Weil-Petersson type metrics
• Asymptotics of Weil-Petersson geodesics. I: Ending laminations, recurrence, and flows
• Word length statistics and Lyapunov exponents for Fuchsian groups with cusps
• Partial sums of excursions along random geodesics and volume asymptotics for thin parts of moduli spaces of quadratic differentials
• The Cantor function
• The Modular Surface and Continued Fractions
• The Weil-Petersson metric geometry
• Quasi-Isometries of Hyperbolic Space are Almost Isometries
• Relatively hyperbolic groups

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