Eigenfunctions with infinitely many isolated critical points

2018/11/09 by Buhovsky, Lev, Logunov, Alexander, Sodin, Mikhail · 1 citation
#35P99 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1811.03835

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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• Coarse nodal counts on sub-Riemannian manifolds

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