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

Abstract

We construct Weil-Petersson (WP) 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 the Masur's criterion for Teichmüller geodesics does not hold for WP geodesics.

34 pages, 5 figures

References in corpus (3)

• Geometry of the Weil-Petersson completion of Teichmüller space
• Hyperbolicity in Teichmüller space
• Slim unicorns and uniform hyperbolicity for arc graphs and curve graphs

Cited by in corpus (2)

• Growth of the Weil-Petersson inradius of moduli space
• Teichmueller flow and Weil-Petersson flow