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2013 On the spectrum of deformations of compact double-sided flat hypersurfaces
Denis Borisov, Pedro Freitas
Anal. PDE 6(5): 1051-1088 (2013). DOI: 10.2140/apde.2013.6.1051

Abstract

We study the asymptotic behavior of the eigenvalues of the Laplace–Beltrami operator on a compact hypersurface in n+1 as it is flattened into a singular double-sided flat hypersurface. We show that the limit spectral problem corresponds to the Dirichlet and Neumann problems on one side of this flat (Euclidean) limit, and derive an explicit three-term asymptotic expansion for the eigenvalues where the remaining two terms are of orders ε2 logε and ε2.

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Denis Borisov. Pedro Freitas. "On the spectrum of deformations of compact double-sided flat hypersurfaces." Anal. PDE 6 (5) 1051 - 1088, 2013. https://doi.org/10.2140/apde.2013.6.1051

Information

Received: 2 May 2012; Revised: 4 October 2012; Accepted: 14 February 2013; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1282.35261
MathSciNet: MR3125550
Digital Object Identifier: 10.2140/apde.2013.6.1051

Subjects:
Primary: 35P15
Secondary: 35J05

Rights: Copyright © 2013 Mathematical Sciences Publishers

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