Abstract
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 language | English (US) |
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Pages (from-to) | 10100-10113 |
Number of pages | 14 |
Journal | International Mathematics Research Notices |
Volume | 2020 |
Issue number | 24 |
DOIs | |
State | Published - Dec 1 2020 |
All Science Journal Classification (ASJC) codes
- General Mathematics