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

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Abstract

Given an arbitrary 1-Lipschitz function f on the torus Tn, we find a k-dimensional subtorus M ⊆ Tn, parallel to the axes, such that the restriction of f to the subtorus M is nearly a constant function. The k-dimensional subtorus M is selected randomly and uniformly. We show that when k ≤ c log n/(log log n + log 1/ε), the maximum and the minimum of f on this random subtorus M differ by at most ε, with high probability.

Original languageEnglish
Pages (from-to)123-131
Number of pages9
JournalLecture Notes in Mathematics
Volume2116
DOIs
StatePublished - 2014

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