Non-branching geodesics and optimal maps in strong CD(K,∞) -spaces
Finna-arvio
Non-branching geodesics and optimal maps in strong CD(K,∞) -spaces
rajalasturmnonbranchinggeodesicsandoptimalmaps.pdf
(Jyväskylän yliopisto - JYX)
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.
Tallennettuna:
Kieli |
englanti |
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Sarja | Calculus of Variations and Partial Differential Equations, 3-4 |
Aiheet | |
ISSN |
0944-2669 |