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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On eigenvalue generic properties of the Laplace-Neumann operator

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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 Antônio Mendonça Marrocos
Support type: Scholarships abroad - Research