Eigenfunctions with infinitely many isolated critical points

Lev Buhovsky; Alexander Logunov; Mikhail Sodin

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arXiv · 1811.03835

Eigenfunctions with infinitely many isolated critical points

Lev Buhovsky·Alexander Logunov·Mikhail Sodin

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Abstract

We construct a Riemannian metric on the $ 2 $-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).

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Lev Buhovsky, Alexander Logunov, Mikhail Sodin. 2018-11-09. Eigenfunctions with infinitely many isolated critical points. https://arxiv.org/abs/1811.03835

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