FIRST EIGENVALUES OF GEOMETRIC OPERATORS UNDER THE YAMABE FLOW

Title & Authors
FIRST EIGENVALUES OF GEOMETRIC OPERATORS UNDER THE YAMABE FLOW
Fang, Shouwen; Yang, Fei;

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 $\small{-{\Delta}_{\phi}+{\frac{R}{2}}}$ under the Yamabe flow, where $\small{{\Delta}_{\phi}}$ is the Witten-Laplacian operator, $\small{{\phi}{\in}C^2(M)}$, 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;
Language
English
Cited by
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