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manuscripta mathematica

, Volume 121, Issue 2, pp 191–200 | Cite as

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

  • Junya TakahashiEmail author
Article

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.

Mathematics Subject Classification (2000)

Primary 58J50 Secondary 35P15 Secondary 53C23 Secondary 58J32 

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Division of Mathematics, Graduate School of Information SciencesTôhoku UniversitySendaiJapan

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