On the spectrum of deformations of compact double-sided flat hypersurfaces
Analysis of PDEs
2016-01-20 v1 Mathematical Physics
math.MP
Spectral Theory
Abstract
We study the asymptotic behaviour of the eigenvalues of the Laplace-Beltrami operator on a compact hypersurface in \mathds{R}^{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 \varepsilon^2\log\varepsilon and \varepsilon^2.
Keywords
Cite
@article{arxiv.1210.4088,
title = {On the spectrum of deformations of compact double-sided flat hypersurfaces},
author = {Denis Borisov and Pedro Freitas},
journal= {arXiv preprint arXiv:1210.4088},
year = {2016}
}