Markov type constants, flat tori and Wasserstein spaces

Vladimir Zolotov

Результат исследований: Научные публикации в периодических изданияхстатья


Let Mp(X, T) denote the Markov type p constant at time T of a metric space X, where p≥ 1. We show that Mp(Y, T) ≤ Mp(X, T) in each of the following cases: (a) X and Y are geodesic spaces and Y is covered by X via a finite-sheeted locally isometric covering, (b) Y is the quotient of X by a finite group of isometries, (c) Y is the Lp-Wasserstein space over X. As an application of (a) we show that all compact flat manifolds have Markov type 2 with constant 1. In particular the circle with its intrinsic metric has Markov type 2 with constant 1. This answers the question raised by S.-I. Ohta and M. Pichot. Parts (b) and (c) imply new upper bounds for Markov type constants of the Lp-Wasserstein space over Rd. These bounds were conjectured by A. Andoni, A. Naor and O. Neiman. They imply certain restrictions on bi-Lipschitz embeddability of snowflakes into such Wasserstein spaces.

Язык оригиналаанглийский
Страницы (с-по)249-263
Число страниц15
ЖурналGeometriae Dedicata
Номер выпуска1
СостояниеОпубликовано - 1 авг 2018

Предметные области Scopus

  • Геометрия и топология

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