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

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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Keywords

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

References

Publication

Received: 11 June 2014

Revised: 5 April 2015

Accepted: 5 May 2015

Published: 23 February 2016

Authors

Babak Modami
Department of Mathematics University of Illinois at Urbana-Champaign 1409 W Green St Urbana, IL 61801 USA

Volume 16, issue 1 (2016)

Babak Modami

Abstract