A rough curvature-dimension condition for metric measure spaces

Anca-Iuliana Bonciocat
2014 Open Mathematics  
AbstractWe 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
more » ... ions as well. For spaces that satisfy a rough curvature-dimension condition we prove a generalized Brunn-Minkowski inequality and a Bonnet-Myers type theorem.
doi:10.2478/s11533-013-0332-7 fatcat:77xpkxfpkvdqjg6acp2hkdpply