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Pálfia Miklós: TBA
Kristály Sándor: Sharp geometric inequalities on non-euclidean settings: an optimal mass transport approach
Based on optimal mass transportation, we present a quick introduction to the theory of CD(K,N) spaces, defined by J. Lott, K.-T. Sturm and C. Villani. [In the setting of Riemannian manifolds the CD(K,N) notion characterizes the objects having Ricci curvature at least K and dimension at most N.] We then prove a sharp isoperimetric inequality in CD(0,N) metric measure spaces assuming an asymptotic volume growth at infinity. As applications of this isoperimetric inequality, we establish Sobolev and Rayleigh-Faber-Krahn inequalities with explicit sharp constants in Riemannian manifolds with nonnegative Ricci curvature; here we also use appropriate symmetrization techniques and optimal volume non-collapsing properties. We also intend to discuss a few aspects of the above problems on Heisenberg groups, which are the simplest sub-Riemannian objects.
For Zoom access please contact E.-Nagy Marianna (marianna.eisenberg-nagy[at]uni-corvinus.hu).