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

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.