# On spectra of hyperbolic surfaces without thin handles

## TL;DR

This paper establishes a precise lower bound for the eigenvalues of the Laplace--Beltrami operator on hyperbolic surfaces with a lower-bounded injectivity radius, advancing understanding of spectral geometry.

## Contribution

It provides a sharp lower estimate on eigenvalues for hyperbolic surfaces with bounded injectivity radius, a novel result in spectral geometry.

## Key findings

- Derived a sharp lower eigenvalue bound for hyperbolic surfaces
- Linked geometric constraints to spectral properties
- Enhanced understanding of spectral behavior in hyperbolic geometry

## Abstract

We obtain a sharp lower estimate on eigenvalues of Laplace--Beltrami operator on a hyperbolic surface with injectivity radius bounded from the below.