Systole and ${\lambda }_{2g-2}$ of a hyperbolic surface

Abstract

We apply topological methods to study eigenvalues of the Laplacian on closed hyperbolic surfaces. For any closed hyperbolic surface $S$ of genus $g$, we get a geometric lower bound on ${\lambda }_{2g-2}(S)$: ${\lambda }_{2g-2}(S)>1/4+{\epsilon }_0(S)$, where ${\epsilon }_0(S)>0$ is an explicit constant which depends only on the systole of $S$

20 pages, 1 figure, To appear in L'enseignement Mathematique

Cited by in corpus (2)

• Small eigenvalues of surfaces of finite type
• Maximal systole of hyperbolic surface with largest $S^3$ extendable abelian symmetry