Year: 2026
Type: preprint
Abstract: We show that any convex co-compact hyperbolic surface with exponent of convergence of Poincaré series $δ\in (\frac25,\frac{14}{27})$ has an essential spectral gap of size $β=\tfrac78(\tfrac12-δ)+\tfrac{1}{32}δ-ε$ for any $ε>0$. In particular, for $δ=\frac12$ this becomes $β=\tfrac{1}{64}-ε$. We show existence of the gap by proving a new Fractal Uncertainty Principle, using a two-ends Furstenberg theorem of O'Regan-Wu-Yi [arXiv:2607.08461].
Source: arXiv (Cornell University)
Authors: Cohen, Alex, Dyatlov, Semyon
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214388693