On the stability operator of submanifolds with constant mean curvature in hyperbolic space (Q1382660)

Let \(M\) be a complete hypersurface with constant mean curvature \(| H | <1\) immersed into hyperbolic \((m+1)\)-space of curvature \(-1\). Let \(\phi: =A- H\cdot \text{Id}\) be the traceless second fundamental form of \(M\) and let \(S: =\Delta +m(1- | H|^2)-| \phi |^2\) be the stability operator in compact subdomains. The author shows, under the assumption that \(M\) has ``finite total curvature'' (i.e., the integral of \(| \phi |^m\) over \(M\) is finite), that the number of eigenvalues of \(S\) less than \(m(1-| H |^2)\) is finite. Moreover, an upper bound in terms of the total curvature of \(M\) is proved.