Collapsing of connected sums and the eigenvalues of the Laplacian

Junya Takahashi

doi:10.1016/S0393-0440(01)00033-X

Collapsing of connected sums and the eigenvalues of the Laplacian

Junya Takahashi

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	201-208
Number of pages	8
Journal	Journal of Geometry and Physics
Volume	40
Issue number	3-4
DOIs	https://doi.org/10.1016/S0393-0440(01)00033-X
Publication status	Published - 2002 Jan 1
Externally published	Yes

Keywords

Collapsing of Riemannian manifolds
Eigenvalue
Laplacian

ASJC Scopus subject areas

Mathematical Physics
Physics and Astronomy(all)
Geometry and Topology

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10.1016/S0393-0440(01)00033-X

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KW - Eigenvalue

KW - Laplacian

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Collapsing of connected sums and the eigenvalues of the Laplacian

Abstract

Keywords

ASJC Scopus subject areas

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