John A. Toth

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20232025

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math.AP2025

$L^{2}$ restriction bounds for analytic continuations of quantum ergodic Laplace eigenfunctions

John A. Toth, Xiao Xiao

We prove a quantum ergodic restriction (QER) theorem for real hypersurfaces $Σ \subset X,$ where $X$ is the Grauert tube associated with a real-analytic, compact Riemannian manifold…

math.AP2024

Non-concentration estimates for Laplace eigenfunctions on compact $C^{\infty}$ manifolds with boundary

Hans Christianson, John A. Toth

Let $Ω$ be an $n$ -dimensional compact Riemannian manifold $(n \geq 3)$ with $C^{\infty}$ boundary, and consider $L^{2}$ -normalized eigenfunctions $- Δ ϕ_{λ} = λ^{2} ϕ_{λ}$ with Dirichlet or…

math.AP2024

Quantum Flux and Quantum Ergodicity for Cross Sections

Hans Christianson, John Toth

For sequences of quantum ergodic eigenfunctions, we define the quantum flux norm associated to a codimension $1$ submanifold $Σ$ of a non-degenerate energy surface. We prove restri…

math.AP2023

Small-scale mass estimates for Neumann eigenfunctions: piecewise smooth planar domains

Hans Christianson, John A. Toth

Let $Ω$ be a piecewise-smooth, bounded convex domain in $R^{2}$ and consider $L^{2}$ -normalized Neumann eigenfunctions $ϕ_{λ}$ with eigenvalue $λ^{2}$ . Our main result is a small-scale {\…

L2 restriction bounds for analytic continuations of quantum ergodic Laplace eigenfunctions

Non-concentration estimates for Laplace eigenfunctions on compact C∞ manifolds with boundary

Quantum Flux and Quantum Ergodicity for Cross Sections

Small-scale mass estimates for Neumann eigenfunctions: piecewise smooth planar domains

$L^{2}$ restriction bounds for analytic continuations of quantum ergodic Laplace eigenfunctions

Non-concentration estimates for Laplace eigenfunctions on compact $C^{\infty}$ manifolds with boundary