Stable minimal hypersurfaces in locally symmetric spaces

LetM be a complete non-compact stable minimal hypersurface in a locally symmetric space N of nonnegative Ricci curvature. We prove that if the integral of square norm of the second fundamental form is finite, i.e., ∫M |A |2dv < ∞, then M must be totally geodesic. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)