Recurrent Weil-Petersson geodesic rays with non-uniquely ergodic ending laminations
@article{Brock2014RecurrentWG, title={Recurrent Weil-Petersson geodesic rays with non-uniquely ergodic ending laminations}, author={Jeffrey F. Brock and Babak Modami}, journal={arXiv: Geometric Topology}, year={2014} }
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.
10 Citations
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Let S = Sg be a closed surface of genus g with g > 2, Mod(S) be the mapping class group of S and Teich(S) be the Teichmüller space of S endowed with the Weil-Petersson metric. Fix X,Y ∈ Teich(S). In…
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We construct a counterexample for an analogue of Masur’s criterion in the setting of Teichmüller space with the Thurston metric. For that, we find a minimal, filling, non-uniquely ergodic lamination…
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