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.
@article{bwmeta1.element.doi-10_2478_s11533-013-0332-7,
author = {Anca-Iuliana Bonciocat},
title = {A rough curvature-dimension condition for metric measure spaces},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {362-380},
zbl = {1290.53052},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0332-7}
}
Anca-Iuliana Bonciocat. A rough curvature-dimension condition for metric measure spaces. Open Mathematics, Tome 12 (2014) pp. 362-380. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0332-7/
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