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.
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