Search results for "optimal mass transportation"

showing 2 items of 2 documents

L∞ estimates in optimal mass transportation

2016

We show that in any complete metric space the probability measures μ with compact and connected support are the ones having the property that the optimal transportation distance to any other probability measure ν living on the support of μ is bounded below by a positive function of the L∞ transportation distance between μ and ν. The function giving the lower bound depends only on the lower bound of the μ-measures of balls centered at the support of μ and on the cost function used in the optimal transport. We obtain an essentially sharp form of this function. In the case of strictly convex cost functions we show that a similar estimate holds on the level of optimal transport plans if and onl…

Sequence010102 general mathematicsta111Function (mathematics)01 natural sciencesUpper and lower boundsComplete metric space010101 applied mathematicsCombinatoricsMetric spaceBounded functionoptimal mass transportationWasserstein distance0101 mathematicsConvex functionAnalysisProbability measureMathematicsJournal of Functional Analysis
researchProduct

Existence of optimal transport maps in very strict CD(K,∞) -spaces

2018

We introduce a more restrictive version of the strict CD(K,∞) -condition, the so-called very strict CD(K,∞) -condition, and show the existence of optimal maps in very strict CD(K,∞) -spaces despite the possible lack of uniqueness of optimal plans. peerReviewed

metric measure spacesdifferentiaaligeometriaRicci curvatureoptimal mass transportationvariaatiolaskentaexistence of optimal mapsmittateoriametriset avaruudetbranching geodesics
researchProduct