Abstract
AbstractIn the present paper, we prove that a lower bound on the 1‐weighted Ricci curvature is equivalent to a convexity of entropies on the Wasserstein space. Based on such characterization, we provide some interpolation inequalities such as the Prékopa–Leindler inequality, the Borel–Branscamp–Lieb inequality, and the Brunn–Minkowski inequality under the curvature bound.
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