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).
|Number of pages||14|
|Journal||International Mathematics Research Notices|
|State||Published - 1 Dec 2020|