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

Babak Modami

Algebraic & Geometric Topology 16 (2016) 267–323

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.

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Teichmüller space, Weil–Petersson metric, ending lamination, strongly asymptotic geodesics, divergent geodesics, stable manifold, Jacobi field
Mathematical Subject Classification 2010
Primary: 30F60, 32G15
Secondary: 37D40
Received: 11 June 2014
Revised: 5 April 2015
Accepted: 5 May 2015
Published: 23 February 2016
Babak Modami
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W Green St
Urbana, IL 61801