Ricci-curvature Lower Bounds and Branching Geodesics
speaker: Tapio Rajala (University of Jyväskylä)abstract: Taking as starting point the metric measure spaces with Ricci-curvature bounded below in the sense of Lott-Villani and Sturm, I will discuss the problem of branching geodesics. Many of the results in these spaces were originally proven under the extra assumption of non-branching. This assumption is not stable when coupled with the Ricci-curvature lower bounds. Recently the assumption of non-branching was removed in some of the results. For instance local Poincaré inequalities hold also in branching spaces. Attacking the problem from a different direction, in a joint work with K.-T. Sturm we have shown that the metric measure spaces with Riemannian Ricci-curvature bounded from below, as defined by L. Ambrosio, N. Gigli and G. Savaré, are essentially non-branching.
timetable:
Mon 5 Nov, 16:50 - 17:40, Aula Dini
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