First eigenvalues of geometric operators under the Ricci flow

Cao, Xiaodong

doi:10.1090/S0002-9939-08-09533-6

First eigenvalues of geometric operators under the Ricci flow
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Proc. Amer. Math. Soc. 136 (2008), 4075-4078 Request permission

Abstract:

In this paper, we prove that the first eigenvalues of $-\Delta + cR$ ($c\geq \frac 14$) 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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