Collapsing to Riemannian manifolds with boundary and the convergence of the eigenvalues of the Laplacian

Junya Takahashi

doi:10.1007/s00229-006-0035-5

Collapsing to Riemannian manifolds with boundary and the convergence of the eigenvalues of the Laplacian

Junya Takahashi

INF - System Information Sciences

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

1 Citation (Scopus)

Abstract

We prove that the eigenvalues of the Laplacian acting on functions converge to those of the limit manifold for a special collapsing family of closed Riemannian manifolds without curvature bounds. The proof uses L ²-analysis.

Original language	English
Pages (from-to)	191-200
Number of pages	10
Journal	manuscripta mathematica
Volume	121
Issue number	2
DOIs	https://doi.org/10.1007/s00229-006-0035-5
Publication status	Published - 2006 Oct 1

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s00229-006-0035-5

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abstract = "We prove that the eigenvalues of the Laplacian acting on functions converge to those of the limit manifold for a special collapsing family of closed Riemannian manifolds without curvature bounds. The proof uses L 2-analysis.",

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Collapsing to Riemannian manifolds with boundary and the convergence of the eigenvalues of the Laplacian

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