Log-scale equidistribution of nodal sets in Grauert tubes

DOI10.1016/j.matpur.2018.12.004zbMath1422.58006arXiv1803.03579OpenAlexW2962780151WikidataQ128767289 ScholiaQ128767289MaRDI QIDQ2274022

Robert Chang, Steven Zelditch

Publication date: 19 September 2019

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.03579

zbMATH Keywords

eigenfunctionquantum ergodicityGrauert tubenodal setsmall-scale

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Kähler manifolds (32Q15) Pseudodifferential and Fourier integral operators on manifolds (58J40) Parametrices in context of PDEs (35A17) Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity (58J51) PDEs on manifolds (35R01)

Cites Work

• Complex zeros of real ergodic eigenfunctions
• \(L^{p}\) norms, nodal sets, and quantum ergodicity
• Grauert tubes and the homogeneous Monge-Ampère equation
• Global solutions of the homogeneous complex Monge-Ampère equation and complex structures on the tangent bundle of Riemannian manifolds
• Grauert tubes and the homogeneous Monge-Ampère equation. II
• Distribution of zeros of random and quantum chaotic sections of positive line bundles
• Log-scale equidistribution of zeros of quantum ergodic eigensections
• Ergodicity and intersections of nodal sets and geodesics on real analytic surfaces
• The currents defined by analytic varieties
• The Tangent Bundle of an Almost Complex Manifold
• Small scale quantum ergodicity in negatively curved manifolds
• Intégration sur un ensemble analytique complexe
• The Spectral Theory of Toeplitz Operators. (AM-99)
• Generic Properties of Eigenfunctions
• Intrinsic microlocal analysis and inversion formulae for the heat equation on compact real-analytic riemannian manifolds
• Pluri-potential theory on Grauert tubes of real analytic Riemannian manifolds, I
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