Spectral Analysis of the Laplacian Operator in Two-Dimensional Strips
Quasilocal conserved quantities and transport in integrable one-dimensional systems
| Full text | |
| Author(s): |
Gomes, V, Jose N.
;
Marrocos, Marcus A. M.
[1]
Total Authors: 2
|
| Affiliation: | [1] Univ Fed ABC, CMCC, Av Estados 5001, BR-09210580 Sao Paulo - Brazil
Total Affiliations: 1
|
| Document type: | Journal article |
| Source: | JOURNAL OF GEOMETRY AND PHYSICS; v. 135, p. 21-31, JAN 2019. |
| Web of Science Citations: | 0 |
| 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 M-k of all C-k Riemannian metrics on M. This implies the existence of a residual set of metrics in M-k, 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. (C) 2018 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 16/10009-3 - On eigenvalues of Laplacian in kahler manifolds |
| Grantee: | Marcus Antonio Mendonça Marrocos |
| Support Opportunities: | Scholarships abroad - Research |