Zonal states and improved $L^\infty$ bounds for eigenfunctions of magnetic Laplacians on hyperbolic surfaces
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917335803101184 |
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| author | Chabert, Ambre Lefeuvre, Thibault |
| author_facet | Chabert, Ambre Lefeuvre, Thibault |
| contents | We establish polynomially improved $L^\infty$ bounds for eigenfunctions of magnetic Laplacians on hyperbolic surfaces in the critical energy regime. We also show that, below the critical energy, the Hörmander 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_12177 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Zonal states and improved $L^\infty$ bounds for eigenfunctions of magnetic Laplacians on hyperbolic surfaces Chabert, Ambre Lefeuvre, Thibault Analysis of PDEs Differential Geometry Spectral Theory 35P20, 81Q10, 37J35, 58J50 We establish polynomially improved $L^\infty$ bounds for eigenfunctions of magnetic Laplacians on hyperbolic surfaces in the critical energy regime. We also show that, below the critical energy, the Hörmander 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. |
| title | Zonal states and improved $L^\infty$ bounds for eigenfunctions of magnetic Laplacians on hyperbolic surfaces |
| topic | Analysis of PDEs Differential Geometry Spectral Theory 35P20, 81Q10, 37J35, 58J50 |
| url | https://arxiv.org/abs/2603.12177 |