A first eigenvalue estimate for embedded hypersurfaces

Suppose that M is a compact orientable hypersurface embedded in a compact n-dimensional orientable Riemannian manifold N. Suppose that the Ricci curvature of N is bounded below by a positive constant k  . We show that 2λ1>k−(n−1)maxM|H|2λ1>k−(n−1)maxM|H| where λ1λ1 is the first eigenvalue of the Laplacian of M and H is the mean curvature of M.