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 2 lambda(1) > k - (n - 1) max(M) vertical bar H vertical bar where lambda(1) is the first eigenvalue of the Laplacian of M and H is the mean curvature of M. (C) 2007 Elsevier B.V. All rights reserved.