#### Shahroud Azami, The first eigenvalue of \$\Delta_p^2-\Delta_p\$ along the Ricci flow, Vol. 2020 (2020), Article ID 30, pp. 1-14

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DOI: 10.23952/jnfa.2020.30

Received October 30, 2019; Accepted July 2, 2020; Published July 14, 2020

Abstract. In this paper, we derive the evolution equations for the first eigenvalue of operator $\Delta_{p}^{2}-\Delta_{p}$ acting on the space of functions on a closed Riemannian manifold along the Ricci flow. We prove that the first nonzero eigenvalue is nondecreasing under the Ricci flow under certain geometric conditions.

Shahroud Azami, The first eigenvalue of $\Delta_p^2-\Delta_p$ along the Ricci flow, Journal of Nonlinear Functional Analysis, Vol. 2020 (2020), Article ID 30, pp. 1-14.