6533b872fe1ef96bd12d3c03

RESEARCH PRODUCT

Non-branching geodesics and optimal maps in strong CD(K,∞) -spaces

Tapio RajalaKarl-theodor Sturm

subject

metric measure spacesoptimal mapssMathematics::Metric GeometryMathematics::Differential Geometrynon-branching geodesic

description

We prove that in metric measure spaces where the entropy functional is Kconvex along every Wasserstein geodesic any optimal transport between two absolutely continuous measures with finite second moments lives on a non-branching set of geodesics. As a corollary we obtain that in these spaces there exists only one optimal transport plan between any two absolutely continuous measures with finite second moments and this plan is given by a map. The results are applicable in metric measure spaces having Riemannian Ricci curvature bounded below, and in particular they hold also for Gromov-Hausdorff limits of Riemannian manifolds with Ricci curvature bounded from below by some constant. peerReviewed

yearjournalcountryeditionlanguage
2014-01-01
http://urn.fi/URN:NBN:fi:jyu-201508182691