Generic spectrum of warped products and G-manifolds
Differential Geometry
2021-05-05 v2 Mathematical Physics
math.MP
Spectral Theory
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.
Keywords
Cite
@article{arxiv.1804.02726,
title = {Generic spectrum of warped products and G-manifolds},
author = {Marcus A. M. Marrocos and José N. V. Gomes},
journal= {arXiv preprint arXiv:1804.02726},
year = {2021}
}
Comments
Final version which has been accepted for publication in The Journal of Geometric Analysis