First Eigenvalues of Geometric Operators under the Ricci Flow

Abstract

In this paper, we prove that the first eigenvalues of $-\Delta +cR$ ($c\ge \frac{1}{4}$) is nondecreasing under the Ricci flow. We also prove the monotonicity under the normalized flow for the case $c=1/4$, and $r\le 0$.

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