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A rough curvature-dimension condition for metric measure spaces

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Bonciocat A.-I.

Open Mathematics

2014

tom 12

nr 2

362-380

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.

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1 Open Mathematics

1 Bonciocat A.-I.

1 2014

Wyniki wyszukiwania

A rough curvature-dimension condition for metric measure spaces