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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

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.

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Teichmüller space, Weil–Petersson metric, recurrent geodesics, non-uniquely ergodic lamination
Mathematical Subject Classification 2010
Primary: 30F60, 32G15
Secondary: 37D40
Received: 21 September 2014
Accepted: 6 April 2015
Published: 6 January 2016
Proposed: Danny Calegari
Seconded: Benson Farb, Jean-Pierre Otal
Jeffrey Brock
Department of Mathematics
Brown University
Box 1917
Providence, RI 02912
Babak Modami
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W Green St
Urbana, IL 61801