Spectral gap for surfaces of infinite volume with negative curvature
Spectral Theory
2026-02-13 v2 Analysis of PDEs
Dynamical Systems
Abstract
We prove that the imaginary parts of scattering resonances for negatively curved asymptotically hyperbolic surfaces are uniformly bounded away from zero and provide a resolvent bound in the resulting resonance-free strip. This provides an essential spectral gap without the pressure condition. This is done by adapting the methods of [arXiv:1004.3361], [arXiv:1012.4391] and [arXiv:2201.08259] and answers a question posed in [arXiv:1504.06589].
Keywords
Cite
@article{arxiv.2403.19550,
title = {Spectral gap for surfaces of infinite volume with negative curvature},
author = {Zhongkai Tao},
journal= {arXiv preprint arXiv:2403.19550},
year = {2026}
}
Comments
Added an appendix discussing the spectral gap for convex cocompact hyperbolic manifolds in higher dimensions