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On Eigenvalue Generic Properties of the ...
Gomes, José N. V....

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On Eigenvalue Generic Properties of the Laplace-Neumann Operator by Gomes, José N. V. ( Author )
Lemonjar Open Access
N.A
23-10-2015
We establish the existence of analytic curves of eigenvalues for the Laplace-Neumann operator through an analytic variation of the metric of a compact Riemannian manifold M with boundary by means of a new approach rather than Kato's method for unbounded operators. We obtain an expression for the derivative of the curve of eigenvalues, which is used as a device to prove that the eigenvalues of the Laplace-Neumann operator are generically simple in the space Mk of all Ck Riemannian metrics on M. This implies the existence of a residual set of metrics in Mk, which make the spectrum of the Laplace-Neumann operator simple. We also give a precise information about the complementary of this residual set, as well as about the structure of the set of the deformation of a Riemannian metric which preserves double eigenvalues.
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English
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MYR 0.00
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https://arxiv.org/abs/1510.07067
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