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Isoperimetric control of the spectrum of a compact hypersurface
-
Bruno Colbois
,
Ahmad El Soufi
Published/Copyright:
April 3, 2012
Abstract.
Upper bounds for the eigenvalues of the Laplace–Beltrami operator on a hypersurface bounding a domain in some ambient Riemannian manifold are given in terms of the isoperimetric ratio of the domain. These results are applied to the extrinsic geometry of isometric embeddings.
Received: 2010-09-25
Revised: 2011-11-16
Published Online: 2012-04-03
Published in Print: 2013-10-01
© 2013 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- Unified approach to the classification of actions of discrete amenable groups on injective factors
- Isoperimetric control of the spectrum of a compact hypersurface
- Weighted divisor sums and Bessel function series. III
- Quasilinear parabolic equations and the Ricci flow on manifolds with boundary
- On the noncommutative Bondal–Orlov conjecture
- Cohomogeneity one actions on symmetric spaces of noncompact type
- Isoparametric functions and exotic spheres
- The rationality of the moduli spaces of trigonal curves of odd genus
- On Nichols algebras of diagonal type
