Duality theory for multi-marginal optimal transport with repulsive costs in metric spaces
نویسندگان
چکیده
منابع مشابه
Approximation of endpoints for multi-valued mappings in metric spaces
In this paper, under some appropriate conditions, we prove some $Delta$ and strong convergence theorems of endpoints for multi-valued nonexpansive mappings using modified Agarwal-O'Regan-Sahu iterative process in the general setting of 2-uniformly convex hyperbolic spaces. Our results extend and unify some recent results of the current literature.
متن کاملRicci Curvature for Metric-measure Spaces via Optimal Transport
We define a notion of a measured length space X having nonnegative N -Ricci curvature, for N ∈ [1,∞), or having ∞-Ricci curvature bounded below by K, for K ∈ R. The definitions are in terms of the displacement convexity of certain functions on the associated Wasserstein metric space P2(X) of probability measures. We show that these properties are preserved under measured Gromov-Hausdorff limits...
متن کاملOptimal Transport and Ricci Curvature for Metric-measure Spaces
We survey work of Lott-Villani and Sturm on lower Ricci curvature bounds for metric-measure spaces. An intriguing question is whether one can extend notions of smooth Riemannian geometry to general metric spaces. Besides the inherent interest, such extensions sometimes allow one to prove results about smooth Riemannian manifolds, using compactness theorems. There is a good notion of a metric sp...
متن کاملCurvature of Hypergraphs via Multi-Marginal Optimal Transport
We introduce a novel definition of curvature for hypergraphs, a natural generalization of graphs, by introducing a multimarginal optimal transport problem for a naturally defined random walk on the hypergraph. This curvature, termed coarse scalar curvature, generalizes a recent definition of Ricci curvature for Markov chains on metric spaces by Ollivier [Journal of Functional Analysis 256 (2009...
متن کاملDecoupling of DeGiorgi-type systems via multi-marginal optimal transport∗
We exhibit a surprising relationship between elliptic gradient systems of PDEs, multi-marginal MongeKantorovich optimal transport problem, and multivariable Hardy-Littlewood inequalities. We show that the notion of an orientable elliptic system, conjectured in [6] to imply that (in low dimensions) solutions with certain monotonicity properties are essentially 1-dimensional, is equivalent to the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ESAIM: Control, Optimisation and Calculus of Variations
سال: 2019
ISSN: 1292-8119,1262-3377
DOI: 10.1051/cocv/2018062