Article Contents
Article Contents

# Improved geodesics for the reduced curvature-dimension condition in branching metric spaces

• In this note we show that in metric measure spaces satisfying the reduced curvature-dimension condition $CD^*(K,N)$ we always have geodesics in the Wasserstein space of probability measures that satisfy the critical convexity inequality of $CD^*(K,N)$ also for intermediate times and in addition the measures along these geodesics have an upper-bound on their densities. This upper-bound depends on the bounds for the densities of the end-point measures, the lower-bound $K$ for the Ricci-curvature, the upper-bound $N$ for the dimension, and on the diameter of the union of the supports of the end-point measures.
Mathematics Subject Classification: Primary: 53C23; Secondary: 28A33, 49Q20.

 Citation:

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