First Eigenvalues of Geometric Operators under the Ricci Flow

Xiaodong Cao

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arXiv · 0710.3947

First Eigenvalues of Geometric Operators under the Ricci Flow

Xiaodong Cao

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Abstract

In this paper, we prove that the first eigenvalues of $-Δ+ cR$ ($c\geq \frac14$) 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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Xiaodong Cao. 2008-01-21. First Eigenvalues of Geometric Operators under the Ricci Flow. https://arxiv.org/abs/0710.3947

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