On nodal sets and nodal domains on S 2 and ℝ 2
Alexandre Erëmenko, Dmitry Jakobson, Nikolaï Nadirashvili · Annales de l’institut Fourier · 2007
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 Δ u = u in ℝ 2 that has only two nodal domains. This equation arises in the study of high energy eigenfunctions.