  We complete the picture of sharp eigenvalue estimates for the p-Laplacian on
a compact manifold by providing sharp estimates on the first nonzero eigenvalue
of the nonlinear operator $\Delta_p$ when the Ricci curvature is bounded from
below by a negative constant. We assume that the boundary of the manifold is
convex, and put Neumann boundary conditions on it. The proof is based on a
refined gradient comparison technique and a careful analysis of the underlying
model spaces.
