Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
11017282 | Journal of Geometry and Physics | 2019 | 15 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
José N.V. Gomes, Marcus A.M. Marrocos,