A rough curvature-dimension condition for metric measure spaces

• Autorzy: Anca-Iuliana Bonciocat
• Języki publikacji: EN

Abstrakty

EN

We introduce and study a rough (approximate) curvature-dimension condition for metric measure spaces, applicable especially in the framework of discrete spaces and graphs. This condition extends the one introduced by Karl-Theodor Sturm, in his 2006 article On the geometry of metric measure spaces II, to a larger class of (possibly non-geodesic) metric measure spaces. The rough curvature-dimension condition is stable under an appropriate notion of convergence, and stable under discretizations as well. For spaces that satisfy a rough curvature-dimension condition we prove a generalized Brunn-Minkowski inequality and a Bonnet-Myers type theorem.

Słowa kluczowe

EN

Optimal transport; Entropy; Wasserstein metric; Curvature-dimension condition; Discrete spaces

Kategorie tematyczne

• 49Q20: Variational problems in a geometric measure-theoretic setting
• 52A38: Length, area, volume
• 60B10: Convergence of probability measures
• 46E27: Spaces of measures
• 28A33: Spaces of measures, convergence of measures

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 2
• Strony: 362-380

Daty

wydano

2014-02-01

online

2013-11-21

Twórcy

autor

Anca-Iuliana Bonciocat

• “Simion Stoilow” Institute of Mathematics of the Romanian Academy of Sciences

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0332-7