Surveys in Differential Geometry

Volume 22 (2017)

Recent progress in quantitative topology

Pages: 191 – 216



Larry Guth (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)


We discuss recent work of Chambers, Dotterrer, Ferry, Manin, and Weinberger, which resolved a fundamental question in quantitative topology: if $f : S^m \to S^n$ is a contractible map with Lipschitz constant $L$, what can we say about the Lipschitz constant of a nullhomotopy of $f$?

Published 13 September 2018