Abstract
We study the asymptotic behavior of the eigenvalues of the Laplace–Beltrami operator on a compact hypersurface in 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 and .
Citation
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
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