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Spectral gaps on negatively curved surfaces

Published on:

28 March 2024

Primary Category:

Spectral Theory

Paper Authors:

Zhongkai Tao

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Key Details

Proves essential spectral gap for surfaces without pressure condition

Adapts methods of Bourgain-Dyatlov, Vasy and Vacossin

Uses quantum monodromy and microlocal analysis

Relies on surfaces having 1D trapped set by Eberlein

Provides resolvent bounds in the resonance-free region

AI generated summary

Spectral gaps on negatively curved surfaces

This paper proves that negatively curved asymptotically hyperbolic surfaces have a uniform lower bound on the imaginary parts of scattering resonances, thus exhibiting an essential spectral gap. This is shown by adapting methods from previous work and answers an open question, without needing the topological pressure condition assumed previously.

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