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

Brock, Jeffrey¹ ; Modami, Babak²

¹ Department of Mathematics, Brown University, Box 1917, Providence, RI 02912, USA
² Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W Green St, Urbana, IL 61801, USA

Geometry & topology, Tome 19 (2015) no. 6, pp. 3565-3601.

Résumé

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.

Détail

DOI : 10.2140/gt.2015.19.3565

Classification : 30F60, 32G15, 37D40
Keywords: Teichmüller space, Weil–Petersson metric, recurrent geodesics, non-uniquely ergodic lamination

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