  In this paper, we give a lower bound for the spectrum of the Laplacian on
minimal hypersurfaces immersed into $H^m \times R$. As an application, in
dimension 2, we prove that a complete minimal surface with finite total
extrinsic curvature has finite index. On the other hand, for stable, minimal
surfaces in $H^3$ or in $H^2 \times \R$, we give an upper bound on the infimum
of the spectrum of the Laplacian and on the volume growth.
