MYERS-TYPE COMPACTNESS THEOREM WITH THE BAKRY-EMERY RICCI TENSOR

초록

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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