The Brunn-Minkowski inequality and its relation with the CD condition
speaker: Mattia Magnabosco (University of Bonn)abstract: The Lott-Sturm-Villani CD condition generalizes, to the setting of metric measure spaces, the notion of having Ricci curvature bounded from below and dimension bounded from above. One of the most important merits of the CD condition is that it is sufficient to deduce some geometric properties and functional inequalities that hold in the smooth world. A good example of this is the Brunn-Minkowski inequality, which, if properly generalized, is implied by the CD condition. In this talk I investigate whether the validity of the Brunn-Minkowski inequality is sufficient to prove the CD condition, showing in particular two results: the equivalence of the two requirements for weighted Riemannian manifolds and a slightly weaker equivalence result that holds in the general setting of metric measure spaces. This is a joint work with Lorenzo Portinale and Tommaso Rossi.
timetable:
Tue 25 Oct, 16:30 - 16:55, Aula Magna Bruno Pontecorvo
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