On the oscillation rigidity of a Lipschitz function on a high-dimensional flat torus

Dmitry Faifman, Bo'az Klartag, Vitali Milman

Given an arbitrary $1$-Lipschitz function $f$ on the torus ${\mathbb{T}}^n$, we find a $k$-dimensional subtorus $M\subseteq {\mathbb{T}}^n$, parallel to the axes, such that the restr…