A geometric uncertainty principle with an application to Pleijel's estimate
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Publication:481792
DOI10.1007/s00023-013-0310-4zbMath1319.35132arXiv1306.3103OpenAlexW3106412381MaRDI QIDQ481792
Publication date: 15 December 2014
Published in: Annales Henri Poincaré (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1306.3103
Estimates of eigenvalues in context of PDEs (35P15) Length, area, volume, other geometric measure theory (28A75) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17)
Related Items (13)
Optimal Gabor frame bounds for separable lattices and estimates for Jacobi theta functions ⋮ On exact Pleijel's constant for some domains ⋮ Pleijel's nodal domain theorem for Neumann and Robin eigenfunctions ⋮ Bounding the number of nodal domains of eigenfunctions without singular points on the square ⋮ On Pleijel's nodal domain theorem for the Robin problem ⋮ Quantitative projections in the Sturm oscillation theorem ⋮ Pleijel's theorem for Schrödinger operators with radial potentials ⋮ On the number of Courant-sharp Dirichlet eigenvalues ⋮ A metric Sturm-Liouville theory in two dimensions ⋮ On the distribution of local extrema in quantum chaos ⋮ Large \(m\) asymptotics for minimal partitions of the Dirichlet eigenvalue ⋮ An extremal property of the hexagonal lattice ⋮ A remark on the numerical integration of harmonic functions in the plane
Cites Work
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- On spectral minimal partitions: a survey
- Nodal domains and spectral minimal partitions
- Faber-Krahn inequalities in sharp quantitative form
- The sharp quantitative isoperimetric inequality
- An optimal partition problem for eigenvalues
- Remarks on the boundary set of spectral equipartitions
- Remarks on courant's nodal line theorem
- Pleijel’s nodal domain theorem for free membranes
- Stability estimates for certain Faber-Krahn,isocapacitary and Cheeger inequalities
- On Pleijel's Nodal Domain Theorem
- Über Unterdeckungen der Ebene durch Kreise.
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