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MYERS-TYPE COMPACTNESS THEOREM WITH THE BAKRY-EMERY RICCI TENSOR
- Authors
- Hwang, Seungsu; Lee, Sanghun
- Issue Date
- 2021
- Publisher
- TOHOKU UNIVERSITY
- Keywords
- Bakry-Emery Ricci curvature; myers theorem; mean curvature comparison theorem; Riccati inequality
- Citation
- TOHOKU MATHEMATICAL JOURNAL, v.73, no.3, pp 421 - 432
- Pages
- 12
- Journal Title
- TOHOKU MATHEMATICAL JOURNAL
- Volume
- 73
- Number
- 3
- Start Page
- 421
- End Page
- 432
- ISSN
- 0040-8735
- Abstract
- In this paper, we first prove the f-mean curvature comparison in a smooth metric measure space when the Bakry-Emery Ricci tensor is bounded below and f is bounded by a linear function of distance. Based on this, we obtain Myers-type compactness theorems by generalizing the results of Cheeger, Gromov, and Taylor andWan to the Bakry-Emery Ricci tensor. Moreover, we improve a result of Soylu by using a weaker condition on a derivative of f.
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