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.