Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (2): 215-230.

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New Estimates of Lower Bound for the First Eigenvalue on Compact Manifolds with Positive Ricci Curvature

He Yue   

  1. Institute of Mathematics, School of Mathematics Sciences, Nanjing Normal University, Nanjing 210023
  • Received:2015-09-01 Revised:2016-01-03 Online:2016-04-25 Published:2016-04-25
  • Supported by:

    Supported by the NSFC (11171158) and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions

Abstract:

In this paper we study the lower bound for the first (closed, or Dirichlet, or Neumann) eigenvalue of the Laplace operator on compact Riemannian manifolds with its Ricci curvature bounded below by nonnegative constant, and give a new estimate of lower bound for the first (closed, or Neumann) eigenvalue and also an easy proof of Ling's an estimate[16]. Although we use Ling's methods on the whole, to some extent we deal with the singularity of test functions and greatly simplify many of the calculations involved. Maybe we provide a new way for estimating eigenvalues.

Key words: Compact Riemannian manifold with positive Ricci curvature, Laplace operator, Lower bounds for the first eigenvalue, Diameter of manifold, Inscribed radius of manifold

CLC Number: 

  • O186.1
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