Asymptotics of Weil–Petersson Geodesics I: Ending Laminations, Recurrence, and Flows
By Jeffrey F. Brock, H. Masur, Yair N. Minsky. 2008
46 citations recorded by the source corpus.
We define an ending lamination for a Weil–Petersson geodesic ray. Despite the lack of a natural visual boundary for the Weil–Petersson metric [Bro2], these ending laminations provide an effective boundary theory that encodes much of its asymptotic CAT(0) geometry. In particular, we prove an ending lamination theorem (Theorem 1.1) for the full-measure set of rays that recur to the thick part, and we show that the association of an ending lamination embeds asymptote classes of recurrent rays into the Gromov-boundary of the curve complex $${\mathcal{C}(S)}$$. As an application, we establish fundamentals of the topological dynamics of the Weil–Petersson geodesic flow, showing density of closed orbits and topological transitivity.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2f9e1176c1faa2a676ff302f7ad692731346762d
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In Applied Mathematics
In Geometry and Topology
- Saul Schleimer
- Matt Clay
- Christopher J. Leininger
- Kasra Rafi
- Juan Souto
- Javier Aramayona
- Samuel J. Taylor
- U. Hamenstaedt
In Mathematical Physics
- Saul Schleimer
- Christopher J. Leininger
- Matt Clay
- Kasra Rafi
- Juan Souto
- Javier Aramayona
- U. Hamenstaedt
- Benson Farb
Citations in the corpus
- Injections of mapping class groups (2008, background): “The needed facts about the Weil–Petersson metric can be found in [20]; more precisely, see Theorem 1.”
- Uniform hyperbolicity of the curve graph via surgery sequences (2013, background): “The relevance of the three axioms is given by the following theorem of Masur and Minsky [12, Theorem 2.3].”