Algebraic & Geometric Topology

Asymptotics of a class of Weil–Petersson geodesics and divergence of Weil–Petersson geodesics

Babak Modami

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We show that the strong asymptotic class of Weil–Petersson geodesic rays with narrow end invariant and bounded annular coefficients is determined by the forward ending laminations of the geodesic rays. This generalizes the recurrent ending lamination theorem of Brock, Masur and Minsky. As an application we provide a symbolic condition for divergence of Weil–Petersson geodesic rays in the moduli space.

Article information

Algebr. Geom. Topol., Volume 16, Number 1 (2016), 267-323.

Received: 11 June 2014
Revised: 5 April 2015
Accepted: 5 May 2015
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30F60: Teichmüller theory [See also 32G15] 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]
Secondary: 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)

Teichmüller space Weil–Petersson metric ending lamination strongly asymptotic geodesics divergent geodesics stable manifold Jacobi field


Modami, Babak. Asymptotics of a class of Weil–Petersson geodesics and divergence of Weil–Petersson geodesics. Algebr. Geom. Topol. 16 (2016), no. 1, 267--323. doi:10.2140/agt.2016.16.267.

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