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Splitting theorems on complete manifolds with Bakry-Émery curvature

In this paper we study some splitting properties on complete noncompact manifolds with smooth measures when $\infty$-dimensional Bakry-Émery Ricci curvature is bounded from below by some negative constant and spectrum of the weighted Laplacian has a positive lower bound. These results extend the cases of Ricci curvature and $m$-dimensional Bakry-Émery Ricci curvature.

preprint2011arXivOpen access
Jia-Yong Wu
math.DG
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Jia-Yong Wu

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