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).
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}
}
Comments
9 pages