March 3, 2026Open Access

A Spectral Gap for Spinors on Hyperbolic Surfaces

Key Points

A uniform spectral gap for the Dirac operator is established across hyperbolic surfaces.
Specific surfaces are constructed with genus approaching infinity, highlighting their unique geometric properties.
The explicit nature of the construction involves a series of spin hyperbolic surfaces, enriching existing mathematical frameworks.
Implications suggest potential advancements in understanding the relationship between geometry and spectral theory.

Abstract

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

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Cite This Study

Adve et al. (Fri,) studied this question.

synapsesocial.com/papers/69a75bf1c6e9836116a2431f https://doi.org/https://doi.org/10.3929/ethz-c-000793540

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