Eigenfunctions with infinitely many isolated critical points
Spectral Theory
2019-07-01 v2 Analysis of PDEs
Abstract
We construct a Riemannian metric on the -dimensional torus, such that for infinitely many eigenvalues of the Laplace-Beltrami operator, a corresponding eigenfunction has infinitely many isolated critical points. A minor modification of our construction implies that each of these eigenfunctions has a level set with infinitely many connected components (i.e., a linear combination of two eigenfunctions may have infinitely many nodal domains).
Cite
@article{arxiv.1811.03835,
title = {Eigenfunctions with infinitely many isolated critical points},
author = {Lev Buhovsky and Alexander Logunov and Mikhail Sodin},
journal= {arXiv preprint arXiv:1811.03835},
year = {2019}
}
Comments
14 pages, IMRN, to appear