Optimal Transportation and Ricci Curvature for Metric Measure Spaces
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Moreover, we introduce a curvature-dimension condition CD(K, N) being more restrictive than the curvature bound Curv(M,d, m) ≥ K. For Riemannian manifolds, CD(K, N) is equivalent to RicM (ξ, ξ) ≥ K · |ξ|2 and dim(M) ≤ N . Condition CD(K,N) implies sharp version of the Brunn-Minkowski inequality, of the Bishop-Gromov volume comparison theorem and of the Bonnet-Myers theorem. Moreover, it allows to construct canonical Dirichlet forms with Gaussian upper and lower bounds for the corresponding heat kernels.
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تاریخ انتشار 2006