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arXiv · 2601.19663

Quantitative FUP and spectral gap for quasi-Fuchsian group

Long Jin·An Zhang·Hong Zhang
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Abstract

We derive an explicit formula for the exponent $\beta$ in the higher-dimensional fractal uncertainty principle (FUP) established by Cohen 2023, quantifying its dependence on the porosity parameter $\nu$ 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.

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Long Jin, An Zhang, Hong Zhang. 2026-01-27. Quantitative FUP and spectral gap for quasi-Fuchsian group. https://arxiv.org/abs/2601.19663

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