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http://dx.doi.org/10.4134/BKMS.b150530

FIRST EIGENVALUES OF GEOMETRIC OPERATORS UNDER THE YAMABE FLOW  

Fang, Shouwen (School of Mathematical Science Yangzhou University)
Yang, Fei (School of Mathematics and physics China University of Geosciences)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.4, 2016 , pp. 1113-1122 More about this Journal
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.
Keywords
eigenvalue; Witten-Laplacian; Yamabe flow;
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