On nodal sets and nodal domains on \mathbf{S^2} and {\mathbb{R}}^{\mathbf{2}}

Name: Work Video:
Duration: 3 min 30 s
Description: We discuss possible topological configurations of nodal sets, in particular the number of their components, for spherical harmonics on S 2 . We also construct a solution of the equation Δu=u in ℝ 2 that has only two nodal domains. This equation arises in the study of high energy eigenfunctions.
Alexandre Erëmenko; Dmitry Jakobson; Nikolaï Nadirashvili
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