On the effects of small perturbation on low energy Laplace eigenfunctions

2021/08/31 by Mukherjee, Mayukh, Saha, Soumyajit · 2 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2108.13874

Abstract

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.

Cited by

• Payne's nodal line conjecture fails on doubly-connected planar domains
• On the nodal domain count under metric perturbations, Courant sharpness and boundary intersections

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