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j. differential geometry 83 (2009) 377-405
 

Summary: j. differential geometry
83 (2009) 377-405
COMPARISON GEOMETRY FOR THE BAKRY-EMERY
RICCI TENSOR
Guofang Wei & Will Wylie
To the memory of Detlef Gromoll
Abstract
For Riemannian manifolds with a measure (M, g, e-f
dvolg) we
prove mean curvature and volume comparison results when the -
Bakry-Emery 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 Bakry-Emery 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, e-f
dvolg), where M is a complete n-dimensional Riemannian manifold with

  

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

 

Collections: Mathematics