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Rigidity of closed metric measure spaces with nonnegative curvature

Differential Geometry 2017-06-27 v1

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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Cite

@article{arxiv.1706.07894,
  title  = {Rigidity of closed metric measure spaces with nonnegative curvature},
  author = {Jia-Yong Wu},
  journal= {arXiv preprint arXiv:1706.07894},
  year   = {2017}
}

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9 pages