The fractal uncertainty principle via Dolgopyat's method in higher dimensions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866911007812616192 |
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| author | Backus, Aidan Leng, James Tao, Zhongkai |
| author_facet | Backus, Aidan Leng, James Tao, Zhongkai |
| contents | We prove a fractal uncertainty principle with exponent $\frac{d}{2} - δ+ \varepsilon$, $\varepsilon > 0$, for Ahlfors--David regular subsets of $\mathbb R^d$ with dimension $δ$ which satisfy a suitable "nonorthogonality condition". This generalizes the application of Dolgopyat's method by Dyatlov--Jin (arXiv:1702.03619) to prove the same result in the special case $d = 1$. As a corollary, we get a quantitative spectral gap for the Laplacian on convex cocompact hyperbolic manifolds of arbitrary dimension with Zariski dense fundamental groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_11708 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The fractal uncertainty principle via Dolgopyat's method in higher dimensions Backus, Aidan Leng, James Tao, Zhongkai Classical Analysis and ODEs Dynamical Systems Spectral Theory 28A80, 35B34, 81Q50 We prove a fractal uncertainty principle with exponent $\frac{d}{2} - δ+ \varepsilon$, $\varepsilon > 0$, for Ahlfors--David regular subsets of $\mathbb R^d$ with dimension $δ$ which satisfy a suitable "nonorthogonality condition". This generalizes the application of Dolgopyat's method by Dyatlov--Jin (arXiv:1702.03619) to prove the same result in the special case $d = 1$. As a corollary, we get a quantitative spectral gap for the Laplacian on convex cocompact hyperbolic manifolds of arbitrary dimension with Zariski dense fundamental groups. |
| title | The fractal uncertainty principle via Dolgopyat's method in higher dimensions |
| topic | Classical Analysis and ODEs Dynamical Systems Spectral Theory 28A80, 35B34, 81Q50 |
| url | https://arxiv.org/abs/2302.11708 |