Monotonicity Properties of the First Eigenvalue of the Laplacian Operator on Ricci Solitons

Xiang Gao, Qiaofang Xing

Abstract


In this paper, we deal with the monotonicity properties of the first eigenvalue of the Laplacian operator on Ricci solitons. Firstly, by using the monotonicity formula of the $\mathcal{F}$ functional, we derive a monotonicity formula of the first eigenvalue of the Laplacian operator on Ricci solitons. Based on this, we also prove an exponential decreasing property of the first eigenvalue.

Keywords


Laplacian operator; Ricci soliton; $\mathcal{F}$ functional

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DOI: http://dx.doi.org/10.26713%2Fjims.v4i2.85

eISSN 0975-5748; pISSN 0974-875X