Algebraic & Geometric Topology

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

Babak Modami

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841109

Digital Object Identifier
doi:10.2140/agt.2016.16.267

Mathematical Reviews number (MathSciNet)
MR3470702

Zentralblatt MATH identifier
1334.30018

Subjects
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.)

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

Citation

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. https://projecteuclid.org/euclid.agt/1510841109


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