Rigidity of closed metric measure spaces with nonnegative curvature

Jia-Yong Wu

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arXiv · 1706.07894

Rigidity of closed metric measure spaces with nonnegative curvature

Jia-Yong Wu

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Abstract

We show that one-dimensional circle is the only case for closed smooth metric measure spaces with nonnegative Bakry-\'{E}mery Ricci curvature whose spectrum of the weighted Laplacian has an optimal positive upper bound. This result extends the work of Hang-Wang in the manifold case (Int. Math. Res. Not. 18 (2007), Art. ID rnm064, 9pp).

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Jia-Yong Wu. 2017-06-24. Rigidity of closed metric measure spaces with nonnegative curvature. https://arxiv.org/abs/1706.07894

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