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Horocycles, lipschitz maps, and laminations

  • James Farre (MPI MiS, Leipzig)
E2 10 (Leon-Lichtenstein)

Abstract

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. This is joint work with Yair Minsky and Or Landesberg.

Antje Vandenberg

MPI for Mathematics in the Sciences Contact via Mail

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