Spectral gap for surfaces of infinite volume with negative curvature

Zhongkai Tao

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arXiv · 2403.19550

Spectral gap for surfaces of infinite volume with negative curvature

Zhongkai Tao

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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].

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BibTeX RIS

Zhongkai Tao. 2024-03-28. Spectral gap for surfaces of infinite volume with negative curvature. https://arxiv.org/abs/2403.19550

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