Eigenfunctions with few critical points.

DOI10.4310/jdg/1214425450zbMath1038.58036OpenAlexW1531681815WikidataQ115193560 ScholiaQ115193560MaRDI QIDQ1609747

Dmitry Jakobson, Nikolai S. Nadirashvili

Publication date: 15 August 2002

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4310/jdg/1214425450

zbMATH Keywords

critical pointLaplacianeigenfunctionWKB

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Boundary value problems for ordinary differential equations (34B99)

Related Items (12)

Topological properties of Neumann domains ⋮ Non-boundedness of the number of super level domains of eigenfunctions ⋮ Isoparametric foliations and critical sets of eigenfunctions ⋮ Upper bound of critical sets of solutions of elliptic equations in the plane ⋮ Critical point asymptotics for Gaussian random waves with densities of any Sobolev regularity ⋮ Quantum unique ergodicity and the number of nodal domains of eigenfunctions ⋮ Critical sets of eigenfunctions of the Laplacian ⋮ Doubling inequalities and critical sets of Dirichlet eigenfunctions ⋮ No repulsion between critical points for planar Gaussian random fields ⋮ The principal eigenfunction of the Dirichlet Laplacian with prescribed numbers of critical points on the upper half of a topological torus ⋮ Nondegeneracy of the eigenvalues of the Hodge Laplacian for generic metrics on 3-manifolds ⋮ Critical points and geometric properties of Green's functions on open surfaces

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