Geometry, Topology and Dynamics Seminar
Kasra Rafi
University of Oklahoma
Thurston's Lipschitz metric on Teichmüller space
Abstract: In 1980's, Thurston introduced an asymmetric metric for
Teichmüller space which we refer to as the Lipschitz metric. For two
marked hyperbolic structures X and Y, the distance between X and Y is
defined to be the logarithm of the infimum of Lipschitz constants of
homeomorphisms from X to Y that are homotopic to the identity.
The geometry of the Lipschitz metric is very rich, as Thurston shows
in his paper. However, many aspects of it have remained unexamined.
There has been a recent spike in interest in understanding and expanding
Thurston's original ideas. We give a survey of what is known and some
new results.
Monday October 24, 2011 at 3:00 PM in SEO 636