Collapsing of connected sums and the eigenvalues of the Laplacian

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9 Citations (Scopus)

Abstract

We study the behavior of the eigenvalues of the Laplacian acting on functions when one side of a connected sum of two closed Riemannian manifolds collapses to a point. We prove that the eigenvalues converge to those of the limit space, by using the method of Anné and Colbois. From this, we obtain a gluing theorem for the eigenvalues.

Original languageEnglish
Pages (from-to)201-208
Number of pages8
JournalJournal of Geometry and Physics
Volume40
Issue number3-4
DOIs
Publication statusPublished - 2002 Jan 1
Externally publishedYes

Keywords

  • Collapsing of Riemannian manifolds
  • Eigenvalue
  • Laplacian

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

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