Existence of optimal transport maps in very strict $CD(K,\infty )$ -spaces

Abstract

We introduce a more restrictive version of the strict $CD(K,\infty )$ -condition, the so-called very strict $CD(K,\infty )$ -condition, and show the existence of optimal maps in very strict $CD(K,\infty )$ -spaces despite the possible lack of uniqueness of optimal plans.

12 pages