Quantitative FUP and spectral gap for quasi-Fuchsian group

Long Jin; An Zhang; Hong Zhang

Quantitative FUP and spectral gap for quasi-Fuchsian group

Classical Analysis and ODEs 2026-01-28 v1 Analysis of PDEs Geometric Topology Spectral Theory

Authors: Long Jin , An Zhang , Hong Zhang

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.

Keywords

fractal uncertainty principle spectral gap quasi-Fuchsian group porosity hyperbolic 3-manifold convex co-compact

Cite

@article{arxiv.2601.19663,
  title  = {Quantitative FUP and spectral gap for quasi-Fuchsian group},
  author = {Long Jin and An Zhang and Hong Zhang},
  journal= {arXiv preprint arXiv:2601.19663},
  year   = {2026}
}

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33pages, 2 figures

Quantitative FUP and spectral gap for quasi-Fuchsian group

Abstract

Keywords

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