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Let M be a complete minimal hypersurface in hyperbolic space H n + 1 ( − 1 ) $\mathbb {H}^{n+1}(-1)$ with constant sectional curvature −1. We prove that if M has a finite index and finite L 2 $L^{2}$ norm of the second fundamental form, then the fundamental tone λ 1 ( M ) $\lambda_{1} (M)$ is bounded above by n 2 $n^{2}$

Fundamental tone of minimal hypersurfaces with finite index in hyperbolic space