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

✍ Scribed by Junya Takahashi

Publisher
Springer
Year
2006
Tongue
English
Weight
143 KB
Volume
121
Category
Article
ISSN
0025-2611

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πŸ“œ SIMILAR VOLUMES

The first eigenvalue of the p-Laplacian
The first eigenvalue of the p-Laplacian on a compact Riemannian manifold
✍ Shigeo Kawai; Nobumitsu Nakauchi πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 135 KB

The ΓΏrst nonlinear eigenvalue of the p-Laplacian (p ΒΏ 2) is investigated for a compact manifold of nonnegative Ricci curvature with or without boundary. Lower bound estimates are given by the diameter or the inscribed radius. The key ingredients in proofs are the formula of Bochner-Weitz onbeck type

Collapsing of connected sums and the eig
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✍ Junya Takahashi πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 72 KB

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 AnnΓ© and Colbois. From this, we obtain a