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.
CITATION STYLE
Faifman, D., Klartag, B., & Milman, V. (2014). On the oscillation rigidity of a lipschitz function on a high-dimensional flat torus. Lecture Notes in Mathematics, 2116, 123–131. https://doi.org/10.1007/978-3-319-09477-9_10
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