On the effects of small perturbation on low energy Laplace eigenfunctions

We investigate several aspects of the nodal geometry and topology of Laplace eigenfunctions, with particular emphasis on the low frequency regime. This includes investigations in and around the Payne property, opening angle estimates of nodal domains, saturation of (fundamental) spectral gaps etc.,...

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Bibliographic Details
Published in:arXiv.org 2022-10
Main Authors: Mukherjee, Mayukh, Saha, Soumyajit
Format: Article
Language:English
Subjects:
Eigenvectors
Euclidean geometry
Geometry
Perturbation
Riemann manifold
Spectral theory
Topology
Online Access:Get full text
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Summary:We investigate several aspects of the nodal geometry and topology of Laplace eigenfunctions, with particular emphasis on the low frequency regime. This includes investigations in and around the Payne property, opening angle estimates of nodal domains, saturation of (fundamental) spectral gaps etc., and behaviour of all of the above under small scale perturbations. We aim to highlight interesting aspects of spectral theory and nodal phenomena tied to ground state/low energy eigenfunctions, as opposed to asymptotic results.
ISSN:2331-8422