In this sense, the Bakry-Émery Ricci tensor is shown to be natural in the context of Riemannian convergence theory. Additionally, Lott showed that if a Riemannian manifold with smooth density arises as a collapsed limit of Riemannian manifolds with a uniform upper bound on diameter and sectional curvature and a uniform lower bound on Ricci curvature, then the lower bound on Ricci curvature is preserved in the limit as a lower bound on Bakry-Émery's Ricci curvature. The comparison geometry of the Bakry-Émery Ricci tensor was taken further in an influential article of Guofang Wei and William Wylie. For instance, if M is a closed and connected Riemannian manifold with positive Bakry-Émery Ricci tensor, then the fundamental group of M must be finite if instead the Bakry-Émery Ricci tensor is negative, then the isometry group of the Riemannian manifold must be finite. In 2003, Lott showed that much of the standard comparison geometry results for the Ricci tensor extend to the Bakry-Émery setting. National Academy of Sciences Award for Scientific Reviewing (with Bruce Kleiner)Ī seminal 1985 article of Dominique Bakry and Michel Émery introduced a generalized Ricci curvature, in which one adds to the usual Ricci curvature the hessian of a function. Alexander von Humboldt Fellowship (1991-1992).In 2009, he moved to University of California, Berkeley. After postdoctoral positions at Harvard University and the Institut des Hautes Études Scientifiques, he joined the faculty at the University of Michigan. in mathematics under the supervision of Isadore Singer. degrees in mathematics and physics from University of California, Berkeley. from the Massachusetts Institute of Technology in 1978 and M.A.
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