Geodesic
Monotonicity of first eigenvalues along the Yamabe flow
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 2, pp. 387-401
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We construct some nondecreasing quantities associated to the first eigenvalue of $-\Delta _\phi +cR$ $(c\geq \frac 12(n-2)/(n-1))$ 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 $-\Delta _\phi + \frac 14 (n/ (n-1))R$ 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.
We construct some nondecreasing quantities associated to the first eigenvalue of $-\Delta _\phi +cR$ $(c\geq \frac 12(n-2)/(n-1))$ 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 $-\Delta _\phi + \frac 14 (n/ (n-1))R$ 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.
DOI : 10.21136/CMJ.2020.0392-19
Classification : 58C40
Keywords: monotonicity; first eigenvalue; Witten-Laplacian operator; Yamabe flow 
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     title = {Monotonicity of first eigenvalues along the {Yamabe} flow},
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Zhang, Liangdi. Monotonicity of first eigenvalues along the Yamabe flow. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 2, pp. 387-401. doi: 10.21136/CMJ.2020.0392-19

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