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The fractal
uncertainty principle via Dolgopyat's method in higher
dimensions
Aidan Backus, James Leng and Zhongkai Tao |
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Vol. 18 (2025), No. 7, 1769–1804
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Abstract |
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We prove a fractal uncertainty principle with exponent , , for Ahlfors–David regular subsets of with dimension which satisfy a suitable “nonorthogonality condition”. This generalizes the application of Dolgopyat’s method by Dyatlov and Jin (2018) to higher dimensions. As a corollary, we get a quantitative essential spectral gap for the Laplacian on convex cocompact hyperbolic manifolds of arbitrary dimension with Zariski-dense fundamental groups. |
Keywords
fractal uncertainty principle, resonances
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Mathematical Subject Classification
Primary: 28A80, 35B34
Secondary: 81Q50
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Milestones
Received: 14 April 2023
Revised: 27 May 2024
Accepted: 20 July 2024
Published: 13 June 2025
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Authors |
| Aidan Backus | |
| Department of Mathematics Brown University Providence, RI United States |
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| James Leng | |
| Department of Mathematics University of California, Los Angeles Los Angeles, CA United States |
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| Zhongkai Tao | |
| Department of Mathematics University of California, Berkeley Berkeley, CA United States |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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