Upper bounds for the first eigenvalue of the laplace operator on complete Riemannian manifolds

Yi-Jung Hsu, Chien Lun Lai

Research output: Contribution to journalArticlepeer-review

Abstract

Let M be a complete Riemannian manifold with infinite volume and Ω be a compact subdomain in M. In this paper we obtain two upper bound estimates for the first eigenvalue of the Laplacian on the punctured manifold M\Ω subject to volume growth and lower bound of Ricci curvature, respectively. The proof hinges on asymptotic behavior of solutions of second order differential equations, the max-min principle and Bishop volume comparison theorem.

Original languageEnglish
Pages (from-to)1257-1265
Number of pages9
JournalTaiwanese Journal of Mathematics
Volume18
Issue number4
DOIs
StatePublished - 1 Jan 2014

Keywords

  • Complete Riemannian manifolds
  • First eigenvalue

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