We develop a full theory for the new class of Optimal Entropy-Transport problems between
nonnegative and finite Radon measures in general topological spaces. These problems …

The theory of curvature-dimension bounds for nonsmooth spaces has several motivations:
the study of functional and geometric inequalities in structures which arc very far from being …

В работе дан обзор исследований последнего десятилетия и приведены новые
результаты по различным новым модификациям классической задачи Канторовича …

VI Bogachev, “Kantorovich problem of optimal transportation of measures: new directions of
research”, Uspekhi Mat. Nauk, 77:5(467) (2022), 3–52; Russian Math. Surveys, 77:5 (2022) …

The goal of the present work is three-fold. The first goal is to set foundational results on
optimal transport in Lorentzian (pre-) length spaces, including cyclical monotonicity, stability …

This is the first of a series of papers devoted to a thorough analysis of the class of gradient
flows in a metric space (X, d) that can be characterized by Evolution Variational Inequalities …

In this paper we study the family of embeddings Φ t of a compact RCD⁎(K, N) space (X, d,
m) into L 2 (X, m) via eigenmaps. Extending part of the classical results [10],[11] known for …

We show that the algebra of cylinder functions in the Wasserstein Sobolev space H 1, q (P p
(X, d), W p, d, m) generated by a finite and positive Borel measure m on the (p, d) …

We introduce the class of bounded variation (BV) functions in a general framework of strictly
local Dirichlet spaces with doubling measure. Under the 2-Poincaré inequality and a weak …

We study quantum Dirichlet forms and the associated symmetric quantum Markov
semigroups on noncommutative $ L^ 2$ spaces. It is known from the work of Cipriani and …