Best Lipschitz maps

Speaker: Georgios DASKALOPOULOS (Brown University)

Abstract:

In a 1998 preprint, Bill Thurston outlined a Teichmueller theory based on maps between hyperbolic surfaces which minimize the Lipschitz constant in their homotopy class (minimum stretch or best Lipschitz maps). In these lectures I'll present joint work with Karen Uhlenbeck where we initiated the analytic study of several of the key concepts appearing in Thurston's work. In particular, I will introduce a special class of best Lipschitz maps called infinity harmonic and their dual geodesic laminations. I will explain how these techniques can be used to explain Thurston's prediction about the duality between best Lipschitz maps and geodesic laminations (max flow min cut principle, convexity and L^0 <--> L^infinity duality). 

I will start by explaining the major ideas in the simpler case of maps into the circle. In the process I will pose several open problems and conjectures that need to be addressed in the future research. I will try to be as elementary as possible assuming only the minimum knowledge of calculus of variations and topology.

Class times:

1. Thursday 17 October, 13:30-15:05;

2. Friday 18 October, 9:50-11:25

3. Monday 21 October, 15:20-16:55

4. Thursday 24 October, 13:30-15:05

Venue: Shuangqing Complex, B725

Zoom （to be confirmed) meeting ID: 405 416 0815, pw: 111111

Class wechat group: