Horospheres, Lipschitz maps, and laminations

  • James Farre (MPI MiS, Leipzig)
Seminargebäude 213 Universität Leipzig (Leipzig)


Every horocycle in a closed hyperbolic surface is dense, and this has been known since the 1940's. We study the behavior of horocycle orbit closures in Z-covers of closed surfaces, and obtain a fairly complete classification of their topology and geometry. The main tool is a solution of a surprisingly delicate geometric optimization problem: finding an optimal Lipschitz map to the circle and the associated lamination of maximal stretch. I will focus on a novel construction of these optimal Lipschitz maps using the orthogeodesic foliation construction. This is joint work with Yair Minsky and Or Landesberg featuring joint work with Aaron Calderon.

12/8/22 4/18/24

Seminar on Algebra and Combinatorics

Universität Leipzig Augusteum - A314

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail