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First eigenvalues of geometric operators under the Ricci flow

Author: Xiaodong Cao
Journal: Proc. Amer. Math. Soc. 136 (2008), 4075-4078
MSC (2000): Primary 58C40; Secondary 53C44
Published electronically: June 2, 2008
MathSciNet review: 2425749
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Abstract: In this paper, we prove that the first eigenvalues of $ -\Delta + cR$ ( $ c\geq \frac14$) are nondecreasing under the Ricci flow. We also prove the monotonicity under the normalized Ricci flow for the cases $ c= 1/4$ and $ r\le 0$.

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Additional Information

Xiaodong Cao
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853-4201

Received by editor(s): October 5, 2007
Published electronically: June 2, 2008
Additional Notes: This research was partially supported by an MSRI postdoctoral fellowship
Communicated by: Chuu-Lian Terng
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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