Quantitative FUP and spectral gap for quasi-Fuchsian group
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912852639481856 |
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| author | Jin, Long Zhang, An Zhang, Hong |
| author_facet | Jin, Long Zhang, An Zhang, Hong |
| contents | We derive an explicit formula for the exponent $β$ in the higher-dimensional fractal uncertainty principle (FUP) established by Cohen 2023, quantifying its dependence on the porosity parameter $ν$ of the Fourier support. This quantitative version of FUP yields an explicit essential spectral gap for convex co-compact hyperbolic 3-manifolds arising from quasi-Fuchsian groups, thereby refining the result of Tao 2025. Our result extends the earlier work of Jin-Zhang 2020 to higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19663 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantitative FUP and spectral gap for quasi-Fuchsian group Jin, Long Zhang, An Zhang, Hong Classical Analysis and ODEs Analysis of PDEs Geometric Topology Spectral Theory We derive an explicit formula for the exponent $β$ in the higher-dimensional fractal uncertainty principle (FUP) established by Cohen 2023, quantifying its dependence on the porosity parameter $ν$ of the Fourier support. This quantitative version of FUP yields an explicit essential spectral gap for convex co-compact hyperbolic 3-manifolds arising from quasi-Fuchsian groups, thereby refining the result of Tao 2025. Our result extends the earlier work of Jin-Zhang 2020 to higher dimensions. |
| title | Quantitative FUP and spectral gap for quasi-Fuchsian group |
| topic | Classical Analysis and ODEs Analysis of PDEs Geometric Topology Spectral Theory |
| url | https://arxiv.org/abs/2601.19663 |