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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.)

Generic Spectrum of Warped Products and G-Manifolds

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Author(s):
Marrocos, Marcus A. M. [1] ; Gomes, Jose N. V. [2, 3]
Total Authors: 2
Affiliation:
[1] Univ Fed ABC, CMCC, Ave Estados, 5001, BR-09210580 Santo Andre, SP - Brazil
[2] Univ Fed Amazonas, Dept Matemat, Ave Gen Rodrigo Octavio, 6200, BR-69080900 Manaus, AM - Brazil
[3] Lehigh Univ, Dept Math, Christmas Saucon Hall, 14 East Packer Ave, Bethlehem, PA 18015 - USA
Total Affiliations: 3
Document type: Journal article
Source: JOURNAL OF GEOMETRIC ANALYSIS; v. 29, n. 4, p. 3124-3134, DEC 2019.
Web of Science Citations: 0
Abstract

In this paper, we establish a kind of splitting theorem for the eigenvalues of a specific family of operators on the base of a warped product. As a consequence, we prove a density theorem for a set of warping functions that makes the spectrum of the Laplacian a warped-simple spectrum. This is then used to study the generic situation of the eigenvalues of the Laplacian on a class of compact G-manifolds. In particular, we give a partial answer to a question posed in 1990 by Steven Zelditch about the generic situation of multiplicity of the eigenvalues of the Laplacian on principal bundles. (AU)

FAPESP's process: 16/10009-3 - On eigenvalues of Laplacian in kahler manifolds
Grantee:Marcus Antônio Mendonça Marrocos
Support type: Scholarships abroad - Research