Sublinear lower bounds of eigenvalues for twisted Laplacian on compact hyperbolic surfaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915247741206528 |
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| author | Gong, Yulin Jin, Long |
| author_facet | Gong, Yulin Jin, Long |
| contents | We investigate the asymptotic spectral distribution of the twisted Laplacian associated with a real harmonic 1-form on a compact hyperbolic surface. In particular, we establish a sublinear lower bound on the number of eigenvalues in a sufficiently large strip determined by the pressure of the harmonic 1-form. Furthermore, following an observation by Anantharaman \cite{nalinideviation}, we show that quantum unique ergodicity fails to hold for certain twisted Laplacians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12666 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sublinear lower bounds of eigenvalues for twisted Laplacian on compact hyperbolic surfaces Gong, Yulin Jin, Long Spectral Theory Analysis of PDEs We investigate the asymptotic spectral distribution of the twisted Laplacian associated with a real harmonic 1-form on a compact hyperbolic surface. In particular, we establish a sublinear lower bound on the number of eigenvalues in a sufficiently large strip determined by the pressure of the harmonic 1-form. Furthermore, following an observation by Anantharaman \cite{nalinideviation}, we show that quantum unique ergodicity fails to hold for certain twisted Laplacians. |
| title | Sublinear lower bounds of eigenvalues for twisted Laplacian on compact hyperbolic surfaces |
| topic | Spectral Theory Analysis of PDEs |
| url | https://arxiv.org/abs/2504.12666 |