PIMS / AMI Seminar-Daniel J. Kelleher

A general framework on Dirichlet spaces is developed to prove a weak form of the Bakry-Emery estimate and study its consequences. In the classical setting of Riemannian manifolds, this is equivalent to having Ricci curvature lower bounds. However, this estimate may be satisfied in situations, like metric graphs, where generalized notions of Ricci curvature lower bounds are not available. Based on Joint work with F. Baudoin.