대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제53권4호
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  • Pages.1113-1122
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  • 2016
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 투고 : 2015.07.06
  • 발행 : 2016.07.31
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초록

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.

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참고문헌

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피인용 문헌

  1. Monotonicity formulas for the first eigenvalue of the weighted p-Laplacian under the Ricci-harmonic flow vol.2019, pp.1, 2019, https://doi.org/10.1186/s13660-019-1961-6