206 citations · 394 across the 45 of their papers we have counts for
Showing 2012 · math.DGShow all
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math.DG2012★ 6 cited
Non-branching geodesics and optimal maps in strong CD(K,{\infty})-spaces
Tapio Rajala, Karl-Theodor Sturm
We prove that in metric measure spaces where the entropy functional is K-convex along every Wasserstein geodesic any optimal transport between two absolutely continuous measures wi…
math.DG2012★ 206 cited
Riemannian Ricci curvature lower bounds in metric measure spaces with -finite measure
Luigi Ambrosio, Nicola Gigli, Andrea Mondino +1
Using techniques of optimal transportation and gradient flows in metric spaces, we extend the notion of Riemannian Curvature Dimension condition introduced (in case…
math.DG2012
Improved geodesics for the reduced curvature-dimension condition in branching metric spaces
Tapio Rajala
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 me…