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

TL;DR

This paper constructs Weil-Petersson geodesic rays with complex ending laminations, demonstrating that certain classical criteria for Teichmüller geodesics do not apply to WP geodesics, revealing new geometric phenomena.

Contribution

It provides explicit examples of WP geodesic rays with non-uniquely ergodic laminations that are recurrent, challenging existing analogies with Teichmüller geodesics.

Findings

Constructed WP geodesic rays with non-uniquely ergodic laminations.

Showed that Masur's criterion does not extend to WP geodesics.

Recurrent WP geodesics can have complex 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 Teichm\"uller geodesics does not hold for WP geodesics.