Czechoslovak Mathematical Journal, first online, pp. 1-15
Monotonicity of first eigenvalues along the Yamabe flow
Received September 6, 2019. Published online October 29, 2020.
Abstract: We construct some nondecreasing quantities associated to the first eigenvalue of $-\Delta_\phi+cR$ $(c\geq\frac12(n-2)/(n-1))$ along the Yamabe flow, where $\Delta_\phi$ is the Witten-Laplacian operator with a $C^2$ function $\phi$. We also prove a monotonic result on the first eigenvalue of $-\Delta_\phi+ \frac14 (n/ (n-1))R$ along the Yamabe flow. Moreover, we establish some nondecreasing quantities for the first eigenvalue of $-\Delta_\phi+cR^a$ with $a\in(0,1)$ along the Yamabe flow.
Keywords: monotonicity; first eigenvalue; Witten-Laplacian operator; Yamabe flow