Bull. Korean Math. Soc. 2016; 53(4): 1113-1122
Printed July 31, 2016
https://doi.org/10.4134/BKMS.b150530
Copyright © The Korean Mathematical Society.
Shouwen Fang and Fei Yang
Yangzhou University, China University of Geosciences
Let $(M,g(t))$ be a compact Riemannian manifold and the metric $g(t)$ evolve by the Yamabe flow. In the paper we derive the evolution for the first eigenvalue of geometric operator $-\Delta_{\phi}+\frac{R}{2}$ under the Yamabe flow, where $\Delta_{\phi}$ is the Witten-Laplacian operator, $\phi\in C^2(M)$, and $R$ is the scalar curvature with respect to the metric $g(t)$. As a consequence, we construct some monotonic quantities under the Yamabe flow.
Keywords: eigenvalue, Witten-Laplacian, Yamabe flow
MSC numbers: 53C21, 53C44
2021; 58(1): 71-111
2018; 55(6): 1691-1701
2018; 55(3): 851-863
2015; 52(4): 1225-1240
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd