Zonal states and improved $L^\infty$ bounds for eigenfunctions of magnetic Laplacians on hyperbolic surfaces
Analysis of PDEs
2026-03-13 v1 Differential Geometry
Spectral Theory
Abstract
We establish polynomially improved bounds for eigenfunctions of magnetic Laplacians on hyperbolic surfaces in the critical energy regime. We also show that, below the critical energy, the H\"ormander bound is saturated by explicit eigenstates, which we call \emph{magnetic zonal states}. These states resemble zonal harmonics on the sphere and equidistribute on Lagrangian tori in phase space.
Cite
@article{arxiv.2603.12177,
title = {Zonal states and improved $L^\infty$ bounds for eigenfunctions of magnetic Laplacians on hyperbolic surfaces},
author = {Ambre Chabert and Thibault Lefeuvre},
journal= {arXiv preprint arXiv:2603.12177},
year = {2026}
}