Work

Resonance counting and spectral gaps for hyperbolic surfaces via Fourier decay

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.17276

Author: Soares, Louis

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7221816849

Cites: 3

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Related to: 10