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Collapsing of connected sums and the eigenvalues of the Laplacian

✍ Scribed by Junya Takahashi

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 72 KB
Volume: 40
Category: Article
ISSN: 0393-0440
DOI: 10.1016/s0393-0440(01)00033-x

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✦ Synopsis

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.

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