%0 Journal Article %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2021 %T Displacement convexity of Entropy and the distance cost Optimal Transportation %A Fabio Cavalletti %A Nicola Gigli %A Flavia Santarcangelo %B Annales de la Faculté des sciences de Toulouse : Mathématiques %V Ser. 6, 30 %P 411–427 %G eng %U https://afst.centre-mersenne.org/articles/10.5802/afst.1679/ %R 10.5802/afst.1679 %0 Journal Article %J Trans. Amer. Math. Soc. %D 2021 %T Independence of synthetic curvature dimension conditions on transport distance exponent %A Afiny Akdemir %A Andrew Colinet %A Robert McCann %A Fabio Cavalletti %A Flavia Santarcangelo %B Trans. Amer. Math. Soc. %V 374 %P 5877–5923 %G eng %U https://doi.org/10.1090/tran/8413 %R 10.1090/tran/8413 %0 Journal Article %D 2019 %T Isoperimetric inequality under Measure-Contraction property %A Fabio Cavalletti %A Flavia Santarcangelo %K Isoperimetric inequality %K Measure-Contraction property %K Optimal transport %K Ricci curvature %X

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.

%V 277 %P 2893 - 2917 %8 2019/11/01/ %@ 0022-1236 %G eng %U https://www.sciencedirect.com/science/article/pii/S0022123619302289 %N 9 %! Journal of Functional Analysis