On nodal sets and nodal domains on \(S^2\) and \(\mathbb R^2\)

DOI10.5802/aif.2335zbMath1178.58012arXivmath/0611627OpenAlexW2656397757WikidataQ56157961 ScholiaQ56157961MaRDI QIDQ2477562

Dmitry Jakobson, Nikolai S. Nadirashvili, Alexandre Eremenko

Publication date: 14 March 2008

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611627

zbMATH Keywords

spherical harmonicLaplaciannodal setsnodal domainstopological configuration

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Quantum chaos (81Q50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Continued fractions and generalizations (11J70) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50)

Related Items

Laplace operators with eigenfunctions whose nodal set is a knot ⋮ On the geometry of random lemniscates ⋮ Some nodal properties of the quantum harmonic oscillator and other Schrödinger operators in ℝ² ⋮ Submanifolds that are level sets of solutions to a second-order elliptic PDE ⋮ Sets of unique continuation for heat equation ⋮ The minimum numbers of nodal domains of spherical Grushin-harmonics ⋮ A. Stern's analysis of the nodal sets of some families of spherical harmonics revisited ⋮ On Spectral Minimal Partitions: the Case of the Sphere ⋮ Some remarks on spherical harmonics ⋮ Critical points and geometric properties of Green's functions on open surfaces

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