First eigenvalues of geometric operators under the Yamabe flow
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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.
Abstract
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.
참고문헌 (17)
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