On Kakeya-Nikodym averages, \(L^p\)-norms and lower bounds for nodal sets of eigenfunctions in higher dimensions

DOI10.4171/JEMS/564zbMath1330.58023arXiv1301.7468MaRDI QIDQ891763

Matthew D. Blair, Christopher D. Sogge

Publication date: 17 November 2015

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.7468

zbMATH Keywords

eigenfunctions\(L^p\) normsKakeya averagesLaplace Beltrami operator on compact manifolds

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Initial value problems for second-order hyperbolic equations (35L15) Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity (58J51) Harmonic analysis and PDEs (42B37)

Related Items (11)

Concentration of Laplace eigenfunctions and stabilization of weakly damped wave equation ⋮ Bilinear Kakeya-Nikodym averages of eigenfunctions on compact Riemannian surfaces ⋮ Focal points and sup-norms of eigenfunctions ⋮ Refined and microlocal Kakeya-Nikodym bounds of eigenfunctions in higher dimensions ⋮ Eigenfunction restriction estimates for curves with nonvanishing geodesic curvatures in compact Riemannian surfaces with nonpositive curvature ⋮ Growth of high \(L^p\) norms for eigenfunctions: an application of geodesic beams ⋮ Localized \(L^{p}\)-estimates of eigenfunctions: a note on an article of Hezari and Rivière ⋮ \(L^{p}\) norms, nodal sets, and quantum ergodicity ⋮ Sharp endpoint estimates for eigenfunctions restricted to submanifolds of codimension 2 ⋮ Logarithmic improvements in \(L^{p}\) bounds for eigenfunctions at the critical exponent in the presence of nonpositive curvature ⋮ Approximating pointwise products of Laplacian eigenfunctions

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