Eigenfunctions with Infinitely Many Isolated Critical Points

Lev Buhovsky, Alexander Logunov, Mikhail Sodin

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We construct a Riemannian metric on the 2D 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).

Original languageEnglish (US)
Pages (from-to)10100-10113
Number of pages14
JournalInternational Mathematics Research Notices
Issue number24
StatePublished - Dec 1 2020

All Science Journal Classification (ASJC) codes

  • General Mathematics


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