Analytical Estimates Characterizing Lower and Bounded Ricci Curvature

Analytical Estimates Characterizing Lower and Bounded Ricci Curvature

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Aaron Naber, Minerva Distinguished Visitor
Fine Hall 224

The first half of this talk will be spent reviewing the basics of doing analysis on manifolds with lower Ricci curvature bounds. We will end by proving some of the heat flow estimates of Bakry-Emery-Ledoux, which are strong enough to characterize manifolds with lower Ricci curvature bounds. The second half of the talk will focus on estimates on the path space of manifolds when two sided Ricci curvature bounds are present. The estimates tell us that two sided Ricci curvature bounds are equivalent to well behaved martingales, which should be understood as the right generalization of the heat flow on path space.