# Existence of homotopies with prescribed Lipschitz constants

4:00 pm Thursday, September 28, 2017
Greg Chambers (Rice)

Abstract: Given Riemannian manifolds $M$ and $N$, consider maps $f: M \rightarrow N$ and $g: M \rightarrow N$ which are homotopic and $L$-Lipschitz. Gromov asked the following question: Does there exist a homotopy from $f$ to $g$ which is itself $L$-Lipschitz? In this talk, I will describe recent work with D. Dotterrer, F. Manin, and S. Weinberger which partially answers this question. I will also outline some interesting applications of our results.