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ICCM 2007 Vol. II 14 Comparison Geometry for the

Summary: ICCM 2007 Vol. II 14
Comparison Geometry for the
Smooth Metric Measure Spaces
Guofang Wei
Will Wylie
For smooth metric measure spaces the Bakry-Emery Ricci tensor is a
natural generalization of the classical Ricci tensor. It occurs naturally in
the study of diffusion processes, Ricci flow, the Sobolev inequality, and
conformal geometry. Recent developments show that many topological
and geometric results for Ricci curvature can be extended to the Bakry-
Emery Ricci tensor. In this article we survey some of these results.
2000 Mathematics Subject Classification: 53C20.
Keywords and Phrases: Bakry-Emery Ricci tensor, Comparison the-
1. Introduction
A smooth metric measure space is a Riemannian manifold with a
measure conformal to the Riemannian measure. Formally it is a triple
, g, e-f


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics