Eigenfunction scarring and improvements in \(L^\infty\) bounds

DOI10.2140/apde.2018.11.801zbMath1386.35307arXiv1703.10248OpenAlexW3123434598MaRDI QIDQ1686237

John A. Toth, Jeffrey Galkowski

Publication date: 21 December 2017

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.10248

zbMATH Keywords

eigenfunctiondefect measuresup norms

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20)

Related Items (9)

Pointwise bounds for joint eigenfunctions of quantum completely integrable systems ⋮ Non-concentration of Schrödinger eigenfunctions along hypersurfaces ⋮ Quantum entanglement and the growth of Laplacian eigenfunctions ⋮ Growth of high \(L^p\) norms for eigenfunctions: an application of geodesic beams ⋮ Improvements for eigenfunction averages: an application of geodesic beams ⋮ Eigenfunction concentration via geodesic beams ⋮ On the growth of eigenfunction averages: microlocalization and geometry ⋮ Defect measures of eigenfunctions with maximal \(L^\infty\) growth ⋮ Local \(L^p\) norms of Schrödinger eigenfunctions on \({\mathbb{S}}^2\)

Cites Work

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• Focal points and sup-norms of eigenfunctions
• Focal points and sup-norms of eigenfunctions II: the two-dimensional case
• Über die Eigenfunktionen auf geschlossenen Riemannschen Mannigfaltigkeiten
• Localized \(L^{p}\)-estimates of eigenfunctions: a note on an article of Hezari and Rivière
• Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds
• Ergodicity and eigenfunctions of the Laplacian
• Uniform distribution of eigenfunctions on compact hyperbolic surfaces
• On the wave equation on a compact Riemannian manifold without conjugate points
• \(L^ \infty\) norms of eigenfunctions of arithmetic surfaces
• Riemannian manifolds with uniformly bounded eigenfunctions
• Riemannian manifolds with maximal eigenfunction growth
• About the blowup of quasimodes on Riemannian manifolds
• The spectral function of an elliptic operator
• Microlocal defect measures
• Exterior Mass Estimates and L2-Restriction Bounds for Neumann Data Along Hypersurfaces
• Riemannian geometry of contact and symplectic manifolds

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