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Eigenfunctions with Infinitely Many Isolated Critical Points

Author(s): Buhovsky, Lev; Logunov, Aleksandr; Sodin, Mikhail

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Abstract: We construct a Riemannian metric on the 2D torus, such that for infinitely many eigen-values 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).
Publication Date: Dec-2020
Electronic Publication Date: 10-Sep-2019
Citation: Buhovsky, Lev, Logunov, Alexander, Sodin, Mikhail. (2020). Eigenfunctions with Infinitely Many Isolated Critical Points. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2020 (10100 - 10113. doi:10.1093/imrn/rnz181
DOI: doi:10.1093/imrn/rnz181
ISSN: 1073-7928
EISSN: 1687-0247
Pages: 10100 - 10113
Type of Material: Journal Article
Version: Author's manuscript

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