The shape of best Lipschitz maps between hyperbolic surfaces
Aaron Calderon (University of Chicago)
Wednesday 27th August 15:00-17:00
Maths 311B
Abstract
How do you measure the difference between two hyperbolic surfaces? In the 80s, Thurston proposed a new version of Teichmüller theory that says to look at the smallest Lipschitz constant of maps between them. He proved that maps with the best possible constant exist, and while they are not unique, minimizers are always rigid along certain geodesics. In this talk, I’ll describe work with Jing Tao in which we coarsely characterize what must (and what can) happen on the rest of the surface.
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