A Spectral Gap for Spinors on Hyperbolic Surfaces
Number Theory
2025-06-23 v1 Differential Geometry
Spectral Theory
Abstract
The purpose of this note is to construct a sequence of spin hyperbolic surfaces with genus going to infinity and with a uniform spectral gap for the Dirac operator. Our construction is completely explicit. In particular, the can be taken to be a tower of covers, with each an arithmetic hyperbolic surface.
Cite
@article{arxiv.2506.17092,
title = {A Spectral Gap for Spinors on Hyperbolic Surfaces},
author = {Anshul Adve and Vikram Giri},
journal= {arXiv preprint arXiv:2506.17092},
year = {2025}
}
Comments
13 pages, comments welcome!