Work

On the effects of small perturbation on low energy Laplace eigenfunctions

Year: 2025

Type: article

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 well-known nodal line conjecture, 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.

Source: Journal of Spectral Theory

DOI: 10.4171/jst/570

Authors: Mayukh Mukherjee, Soumyajit Saha

Institutions: Indian Institute of Technology Bombay, Université de Strasbourg

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Iowa State University, Council of Scientific and Industrial Research, India, HORIZON EUROPE European Research Council

Award: Integrating Spectral and Geometric data on Moduli Space