Lower bounds for nodal sets of eigenfunctions

Abstract

We prove lower bounds for the Hausdorff measure of nodal sets of eigenfunctions.

To appear in Communications in Mathematical Physics; revised to include two additional references and update bibliographic information

References in corpus (1)

• Local Asymmetry and the Inner Radius of Nodal Domains

Cited by in corpus (26)

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• New applications of Min-max Theory
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• Applications of small scale quantum ergodicity in nodal sets
• Nodal sets of Robin and Neumann eigenfunctions
• Geometry and interior nodal sets of Steklov eigenfunctions
• Quantum ergodicity and $L^p$ norms of restrictions of eigenfunctions
• Doubling inequality and nodal sets for solutions of bi-Laplace equations
• Remarks on nodal volume statistics for regular and chaotic wave functions in various dimensions
• Upper bounds of nodal sets for eigenfunctions of eigenvalue problems
• Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold
• Critical set of eigenfunctions of the Laplacian
• Interior nodal sets of Steklov eigenfunctions on surfaces
• Lower bounds for interior nodal sets of Steklov eigenfunctions
• Semiclassical Cauchy Estimates and Applications
• Lower bounds for nodal set of biharmonic Steklov problems
• Measure Upper Bounds for Nodal Sets of Eigenfunctions of the bi-Harmonic Operator
• Lower bounds for nodal sets of Dirichlet and Neumann eigenfunctions
• Lower bounds on nodal sets of eigenfunctions via the heat flow
• Nodal lengths of eigenfunctions in the disc
• Topological Properties of Neumann Domains
• Distribution of the nodal sets of eigenfunctions on analytic manifolds
• Local $L^p$ norms of Schr{ö}dinger eigenfunctions on ${\mathbb{S}}^2$
• Local Extrema in Quantum Chaos