01032nas a2200205 4500008004100000020001400041245006400055210006300119260001600182300001600198490000800214520038000222653002900602653003300631653002200664653002000686100002200706700002600728856007200754 2019 eng d a0022-123600aIsoperimetric inequality under Measure-Contraction property0 aIsoperimetric inequality under MeasureContraction property c2019/11/01/ a2893 - 29170 v2773 a
We prove that if (X,d,m) is an essentially non-branching metric measure space with m(X)=1, having Ricci curvature bounded from below by K and dimension bounded above by N∈(1,∞), understood as a synthetic condition called Measure-Contraction property, then a sharp isoperimetric inequality à la Lévy-Gromov holds true. Measure theoretic rigidity is also obtained.
10aIsoperimetric inequality10aMeasure-Contraction property10aOptimal transport10aRicci curvature1 aCavalletti, Fabio1 aSantarcangelo, Flavia uhttps://www.sciencedirect.com/science/article/pii/S0022123619302289