6533b85cfe1ef96bd12bcb74

RESEARCH PRODUCT

Equivalent definitions of very strict $CD(K,N)$ -spaces

Timo Schultz

subject

Mathematics - Differential Geometrymetric measure spacesdifferentiaaligeometriaRicci curvatureMathematics - Metric Geometryoptimal transportDifferential Geometry (math.DG)Optimal transportFOS: MathematicsMetric Geometry (math.MG)Geometry and Topology53C23Metric measure spaces

description

We show the equivalence of the definitions of very strict $CD(K,N)$ -condition defined, on one hand, using (only) the entropy functionals, and on the other, the full displacement convexity class $\mathcal{DC}_N$. In particular, we show that assuming the convexity inequalities for the critical exponent implies it for all the greater exponents. We also establish the existence of optimal transport maps in very strict $CD(K,N)$ -spaces with finite $N$.

yearjournalcountryeditionlanguage
2023-01-01
https://dx.doi.org/10.48550/arxiv.1906.07693