Recurrent Weil–Petersson geodesic rays with non-uniquely ergodic ending laminations

Brock, Jeffrey; Modami, Babak

doi:10.2140/gt.2015.19.3565

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Recurrent Weil–Petersson geodesic rays with non-uniquely ergodic ending laminations

Jeffrey Brock and Babak Modami

Geometry & Topology 19 (2015) 3565–3601

DOI: 10.2140/gt.2015.19.3565

Abstract

We construct Weil–Petersson geodesic rays with minimal filling non-uniquely ergodic ending lamination which are recurrent to a compact subset of the moduli space of Riemann surfaces. This construction shows that an analogue of Masur’s criterion for Teichmüller geodesics does not hold for Weil–Petersson geodesics.

Keywords

Teichmüller space, Weil–Petersson metric, recurrent geodesics, non-uniquely ergodic lamination

Mathematical Subject Classification 2010

Primary: 30F60, 32G15

Secondary: 37D40

References

Publication

Received: 21 September 2014

Accepted: 6 April 2015

Published: 6 January 2016

Proposed: Danny Calegari

Seconded: Benson Farb, Jean-Pierre Otal

Authors

Jeffrey Brock
Department of Mathematics Brown University Box 1917 Providence, RI 02912 USA

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

Volume 19, issue 6 (2015)