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

Abstract

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

The final version of this article will be published in the Duke Mathematical Journal

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• Cheeger bounds on spin-two fields
• Sharp eigenvalue estimates on degenerating surfaces
• Degenerating hyperbolic surfaces and spectral gaps for large genus
• Multiplicity of singular solutions to the fractional Yamabe problem on spheres