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

2015/12/27 by Zeng, Fanqi, He, Qun, Chen, Bin
#53C21 #53C44 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1512.08158

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≠0, We derive monotonicity of the lowest eigenvalue of Laplacian-type operator -Δ+cR which generalizes some results of Cao \citeCao2007. For c=0, We derive monotonicity of the first eigenvalue of Laplacian which generalizes some results of Ma \citeMa2006. Moreover, we prove that when (M₃, g₀) is a closed three manifold with positive Ricci curvature, the eigenvalue of the Laplacian diverges as t → T on a limited maximal time in terval [0, T), which generalizes some results of Cerbo and Fabrizio \citeFabrizio2007.

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