 
Summary: j. differential geometry
83 (2009) 377405
COMPARISON GEOMETRY FOR THE BAKRYEMERY
RICCI TENSOR
Guofang Wei & Will Wylie
To the memory of Detlef Gromoll
Abstract
For Riemannian manifolds with a measure (M, g, ef
dvolg) we
prove mean curvature and volume comparison results when the 
BakryEmery Ricci tensor is bounded from below and f or f is
bounded, generalizing the classical ones (i.e. when f is constant).
This leads to extensions of many theorems for Ricci curvature
bounded below to the BakryEmery Ricci tensor. In particular,
we give extensions of all of the major comparison theorems when
f is bounded. Simple examples show the bound on f is necessary
for these results.
1. Introduction
In this paper we study smooth metric measure spaces (Mn, g, ef
dvolg), where M is a complete ndimensional Riemannian manifold with
