Spectral Distribution of Twisted Laplacian on Typical Hyperbolic Surfaces of High Genus
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909243832008704 |
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| author | Gong, Yulin |
| author_facet | Gong, Yulin |
| contents | We investigate the spectral distribution of the twisted Laplacian associated with uniform square-integrable bounded harmonic 1-form on typical hyperbolic surfaces of high genus. First, we estimate the spectral distribution by the supremum norm of the corresponding harmonic form. Subsequently, we show that the square-integrable bounded harmonic form exhibits a small supremum norm for typical hyperbolic surfaces of high genus. Based on these findings, we prove a uniform Weyl law for the distribution of real parts of the spectrum on typical hyperbolic surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_16121 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spectral Distribution of Twisted Laplacian on Typical Hyperbolic Surfaces of High Genus Gong, Yulin Spectral Theory Mathematical Physics Dynamical Systems Geometric Topology We investigate the spectral distribution of the twisted Laplacian associated with uniform square-integrable bounded harmonic 1-form on typical hyperbolic surfaces of high genus. First, we estimate the spectral distribution by the supremum norm of the corresponding harmonic form. Subsequently, we show that the square-integrable bounded harmonic form exhibits a small supremum norm for typical hyperbolic surfaces of high genus. Based on these findings, we prove a uniform Weyl law for the distribution of real parts of the spectrum on typical hyperbolic surfaces. |
| title | Spectral Distribution of Twisted Laplacian on Typical Hyperbolic Surfaces of High Genus |
| topic | Spectral Theory Mathematical Physics Dynamical Systems Geometric Topology |
| url | https://arxiv.org/abs/2306.16121 |