L2 harmonic forms and stability of hypersurfaces with constant mean curvature

We prove that a complete noncompact oriented strongly stable hypersurface M-n with cmc (constant mean curvature) H in a complete oriented manifold Nn+1 with bi-Ricci curvature, satisfying b-Ric(u, v) greater than or equal to n(2)(n-5)/4 H-2 along M, admits no nontrivial L-2 harmonic l-forms. This implies if M-n (2 less than or equal to n less than or equal to 4) is a complete noncompact strongly stable hypersurface in hyperbolic space Hn+1(-1) with cmc H (H-2 L greater than or equal to 4(2n-1)/(5-n)n(2)), there exist no nontrivial L-2 harmonic l-forms on M. We also classify complete oriented strongly stable surfaces with cmc H in a complete oriented manifold N-3 with scalar curvature (S) over tilde satisfying inf(M) (S) over tilde greater than or equal to - 3H(2).