# Nodal sets of Laplace eigenfunctions under small perturbations

@article{Mukherjee2020NodalSO, title={Nodal sets of Laplace eigenfunctions under small perturbations}, author={Mayukh Mukherjee and Soumyajit Saha}, journal={Mathematische Annalen}, year={2020}, volume={383}, pages={475 - 491} }

We study the stability properties of nodal sets of Laplace eigenfunctions on compact manifolds under specific small perturbations. We prove that nodal sets are fairly stable if such perturbations are relatively small, more formally, supported at a sub-wavelength scale. We do not need any generic assumption on the topology of the nodal sets or the simplicity of the Laplace spectrum. As an indirect application, we are able to show that a certain “Payne property” concerning the second nodal set…

## 5 Citations

### Sharp lower bound on the"number of nodal decomposition"of graphs

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The lower bound on the number of nodal decomposition of eigenvectors in the class of all graphs with a fixed number of vertices which can be treated as a discrete analogue to the results of Stern and Lewy in the continuous Laplacian case is discussed.

### Nodal Set Openings on Perturbed Rectangular Domains

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. We study the eﬀects of perturbing the boundary of a rectangle on the nodal sets of eigenfunctions of the Laplacian. Namely, for a rectangle of a given aspect ratio N , we identify the ﬁrst…

### Some applications of heat flow to Laplace eigenfunctions

- MathematicsCommunications in Partial Differential Equations
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Abstract We consider mass concentration properties of Laplace eigenfunctions that is, smooth functions satisfying the equation on a smooth closed Riemannian manifold. Using a heat diffusion…

### NODAL GEOMETRY AND TOPOLOGY OF LOW ENERGY EIGENFUNCTIONS

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We investigate various aspects of the nodal geometry and topology of Laplace eigenfunctions on compact Riemannian manifolds and bounded Euclidean domains, with particular emphasis on the low…

### On the effects of small perturbation on low energy Laplace eigenfunctions

- Physics
- 2021

. 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…

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