Title

Comparison Geometry for the Bakry-Emery Ricci Tensor

Author(s)/Creator(s)

Guofang Wei, University of California - Santa BarbaraFollow
William Wylie, University of California - Los AngelesFollow

Document Type

Article

Date

9-14-2007

Disciplines

Mathematics

Description/Abstract

For Riemannian manifolds with a measure (M, g, e^−fdvol_g) we prove mean curvature and volume comparison results when the 1-Bakry-Emery Ricci tensor is bounded from below and f is bounded or Theta_rf is bounded from below, 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.

Additional Information

This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/0706.1120

Recommended Citation

Wei, Guofang and Wylie, William, "Comparison Geometry for the Bakry-Emery Ricci Tensor" (2007). Mathematics - All Scholarship. 126.
https://surface.syr.edu/mat/126

Source

Harvested from arXiv.org

Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 License.