Small scale quantum ergodicity in negatively curved manifolds

Abstract

The main theorem has been slightly generalized to include a larger class of symbols.

22 pages

References in corpus (2)

• $L^p$ norms, nodal sets, and quantum ergodicity
• Localized $L^p$-estimates of eigenfunctions: A note on an article of Hezari and Rivière

Cited by in corpus (20)

• Planck-scale mass equidistribution of toral Laplace eigenfunctions
• Quantum ergodicity and Benjamini-Schramm convergence of hyperbolic surfaces
• Equidistribution in Shrinking Sets and L^4-Norm Bounds for Automorphic Forms
• $L^p$ norms, nodal sets, and quantum ergodicity
• Small scale equidistribution of random eigenbases
• Nodal Statistics of Planar Random Waves
• Applications of small scale quantum ergodicity in nodal sets
• CLT for Planck scale mass distribution of toral Laplace eigenfunctions
• Localized $L^p$-estimates of eigenfunctions: A note on an article of Hezari and Rivière
• Log-scale equidistribution of zeros of quantum ergodic eigensections
• Mass distribution for toral eigenfunctions via Bourgain's de-randomisation
• Small scale equidistribution for a point scatterer on the torus
• Small scale quantum ergodicity in cat maps. I
• Non-concentration and restriction bounds for Neumann eigenfunctions of piecewise $C^{\infty }$ bounded planar domains
• Sharp endpoint estimates for eigenfunctions restricted to submanifolds of codimension 2
• Average $L^q$ growth and nodal sets of eigenfunctions of the Laplacian on surfaces
• Distribution of the nodal sets of eigenfunctions on analytic manifolds
• Quantum ergodicity for shrinking balls in arithmetic hyperbolic manifolds
• Equidistribution of random waves on small balls
• Semiclassical behaviour of quantum eigenstates