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arXiv · 2610.17276

Resonance counting and spectral gaps for hyperbolic surfaces via Fourier decay

Louis Soares
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Abstract

We prove an improved fractal Weyl upper bound for resonances of infinite-area convex cocompact hyperbolic surfaces, expressed in terms of the Hausdorff dimension of the limit set and the Fourier decay exponent of the Patterson--Sullivan measure. This bound also yields a sharper upper bound for the essential spectral gap for these surfaces.

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Louis Soares. 2026-10-12. Resonance counting and spectral gaps for hyperbolic surfaces via Fourier decay. https://arxiv.org/abs/2610.17276

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