Tohoku Mathematical Journal
2023
December
SECOND SERIES VOL. 75, NO. 4

Tohoku Math. J.
75 (2023), 483-507

Title OPTIMAL MAPS AND LOCAL-TO-GLOBAL PROPERTY IN NEGATIVE DIMENSIONAL SPACES WITH RICCI CURVATURE BOUNDED FROM BELOW

Author Mattia Magnabosco and Chiara Rigoni

(Received July 8, 2021, revised December 2, 2021)
Abstract. In this paper we investigate two important properties of metric measure spaces satisfying the reduced curvature-dimension condition for negative values of the dimension parameter: the existence of a transport map between two suitable marginals and the so-called local-to-global property.

Mathematics Subject Classification. Primary 30L99; Secondary 49N99.
Key words and phrases. Optimal transport maps, local-to-global property, CD spaces, negative dimension.

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