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arXiv · 2506.17092

A Spectral Gap for Spinors on Hyperbolic Surfaces

Anshul Adve·Vikram Giri
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Abstract

The purpose of this note is to construct a sequence of spin hyperbolic surfaces $\Sigma_n$ with genus going to infinity and with a uniform spectral gap for the Dirac operator. Our construction is completely explicit. In particular, the $\Sigma_n$ can be taken to be a tower of covers, with each $\Sigma_n$ an arithmetic hyperbolic surface.

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Anshul Adve, Vikram Giri. 2025-06-20. A Spectral Gap for Spinors on Hyperbolic Surfaces. https://arxiv.org/abs/2506.17092

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