A rough curvature-dimension condition for metric measure spaces |
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Authors: | Anca-Iuliana Bonciocat |
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Institution: | 1. “Simion Stoilow” Institute of Mathematics of the Romanian Academy of Sciences, P.O. Box 1-764, Bucharest, 014700, Romania
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Abstract: | 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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