On eigenvalue generic properties of the Laplace-Neumann operator

Autor(es)

Gomes, V, Jose N. ; Marrocos, Marcus A. M. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Fed ABC, CMCC, Av Estados 5001, BR-09210580 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF GEOMETRY AND PHYSICS; v. 135, p. 21-31, JAN 2019.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 16/10009-3 - Sobre os autovalores do laplaciano em variedades de Kahler
• Beneficiário: Marcus Antonio Mendonça Marrocos
• Modalidade de apoio: Bolsas no Exterior - Pesquisa