Lower bounds on the Hausdorff measure of nodal sets. II

DOI10.4310/MRL.2012.v19.n6.a14zbMath1283.58020arXiv1208.2045OpenAlexW4255510024MaRDI QIDQ390225

Christopher D. Sogge, Steven Zelditch

Publication date: 22 January 2014

Published in: Mathematical Research Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.2045

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50)

Related Items (17)

Equidistribution of the conormal cycle of random nodal sets ⋮ Some remarks on nodal geometry in the smooth setting ⋮ On Kakeya-Nikodym averages, \(L^p\)-norms and lower bounds for nodal sets of eigenfunctions in higher dimensions ⋮ Applications of small-scale quantum ergodicity in nodal sets ⋮ Nodal sets of Laplace eigenfunctions: polynomial upper estimates of the Hausdorff measure ⋮ Nodal sets of Laplace eigenfunctions: proof of Nadirashvili's conjecture and of the lower bound in Yau's conjecture ⋮ \(L^{p}\) norms, nodal sets, and quantum ergodicity ⋮ Geometry and interior nodal sets of Steklov eigenfunctions ⋮ Some nodal properties of the quantum harmonic oscillator and other Schrödinger operators in ℝ² ⋮ Nodal Sets of Laplace Eigenfunctions: Estimates of the Hausdorff Measure in Dimensions Two and Three ⋮ Zero set structure of real analytic Beltrami fields ⋮ A metric Sturm-Liouville theory in two dimensions ⋮ Typical field lines of Beltrami flows and boundary field line behaviour of Beltrami flows on simply connected, compact, smooth manifolds with boundary ⋮ On the distribution of local extrema in quantum chaos ⋮ Indeterminacy estimates and the size of nodal sets in singular spaces ⋮ Lower bounds for interior nodal sets of Steklov eigenfunctions ⋮ Semiclassical Cauchy estimates and applications

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