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Comparison geometry for the bakry-emery ricci tensor

Guofang Wei University of California Will Wylie University of California

Differential Geometry mathscidoc:1609.10144

Journal of Differential Geometry, 83, (2), 377-405, 2009
For Riemannian manifolds with a measure (M, g, e.fdvolg) we prove mean curvature and volume comparison results when the亣- 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.
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@inproceedings{guofang2009comparison,
  title={COMPARISON GEOMETRY FOR THE BAKRY-EMERY RICCI TENSOR},
  author={Guofang Wei, and Will Wylie},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911202305752851801},
  booktitle={Journal of Differential Geometry},
  volume={83},
  number={2},
  pages={377-405},
  year={2009},
}
Guofang Wei, and Will Wylie. COMPARISON GEOMETRY FOR THE BAKRY-EMERY RICCI TENSOR. 2009. Vol. 83. In Journal of Differential Geometry. pp.377-405. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911202305752851801.
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