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arXiv · 1904.08698

Myers-type compactness theorem with the Bakry-Emery Ricci tensor

Seungsu Hwang·Sanghun Lee
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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 from below and $|f|$ is bounded. Based on this, we define a Myers-type compactness theorem by generalizing the results of Cheeger, Gromov, and Taylor and of Wan for the Bakry-Emery Ricci tensor. Moreover, we improve a result from Soylu by using a weaker condition on a derivative $f'(t)$.

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Seungsu Hwang, Sanghun Lee. 2019-04-18. Myers-type compactness theorem with the Bakry-Emery Ricci tensor. https://arxiv.org/abs/1904.08698

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