Sharp inequalities between Zolotarev and Wasserstein distances in ${\mathrm{P}}_2({\mathbb{R}}^d)$

Karol Bołbotowski, Guy Bouchitté

Based on a new Kantorovich-Rubinstein duality principle for the Hessian that was recently established by the two authors, we extend the Rio inequality to any dimension $d\ge 1$ wi…