Pour toute surface hyperbolique de genre $g$, $\lambda_{2g-2}>\frac 14}$

TL;DR

This paper proves that for any hyperbolic surface of genus g, the (2g-2)-th eigenvalue of the Laplace operator exceeds 1/4, providing a universal spectral bound related to surface topology.

Contribution

It establishes a new universal lower bound for a specific Laplace eigenvalue on hyperbolic surfaces of arbitrary genus, linking spectral properties to topology.

Findings

Eigenvalue λ_{2g-2} > 1/4 for all hyperbolic surfaces of genus g

Universal spectral bound independent of surface geometry

Advances understanding of spectral geometry in hyperbolic surfaces

Abstract

We show that for any hyperbolic surface of genus g, the eigenvalue $\lambda _{2g-2}$ of the Laplace operator is > 1/4.