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arXiv · 1202.6514

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

Tapio Rajala
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Abstract

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.

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Tapio Rajala. 2012-02-29. Improved geodesics for the reduced curvature-dimension condition in branching metric spaces. https://arxiv.org/abs/1202.6514

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