Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Yongquan Zhang
Affiliation:

MPIM
Date:

Thu, 16/12/2021 - 15:00 - 16:00 Meeting ID: 931 7291 0947

For passcode contact Christian Kaiser (kaiser@mpim-bonn.mpg.de)

Given a measured geodesic lamination L on a hyperbolic surface, does there exist an infinite geodesic ray with finite transverse measure with resepct to L? Geodesic rays eventually disjoint from L or asymptotic to a leaf of L are obvious candidates, but are there others? In this talk, I will discuss joint work with Tina Torkaman which shows that the answer to the question above is always yes, provided that L is not a multicurve. The proof is based on a symbolic coding scheme coming from a squence of train tracks that carry L. As an application, I will relate the existence of such geodesic rays to the existence of certain geodesic planes in a quasifuchsian manifold, which are disjoint from the convex core, limiting on the convex core, but cannot be separated from the core by a supporting plane of the convex core boundary.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/158