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arXiv · 1512.08158

Monotonicity of eigenvalues of geometric operaters along the Ricci-Bourguignon flow

Fanqi Zeng·Qun He·Bin Chen
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Abstract

In this paper, we study monotonicity of eigenvalues of Laplacian-type operator $-Δ+cR$, where $c$ is a constant, along the Ricci-Bourguignon flow. For $c\neq0$, We derive monotonicity of the lowest eigenvalue of Laplacian-type operator $-Δ+cR$ which generalizes some results of Cao \cite{Cao2007}. For $c=0$, We derive monotonicity of the first eigenvalue of Laplacian which generalizes some results of Ma \cite{Ma2006}. Moreover, we prove that when $(M_{3}, g_{0})$ is a closed three manifold with positive Ricci curvature, the eigenvalue of the Laplacian diverges as $t \rightarrow T$ on a limited maximal time in terval $[0, T)$, which generalizes some results of Cerbo and Fabrizio \cite{Fabrizio2007}.

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Fanqi Zeng, Qun He, Bin Chen. 2015-12-27. Monotonicity of eigenvalues of geometric operaters along the Ricci-Bourguignon flow. https://arxiv.org/abs/1512.08158

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