On the mean curvatures sharp estimates of hypersurfaces (Q699007)

Let \(N\) be a hypersurface of a Riemannian manifold \(M\) and denote the principal curvatures by \(k_1, \cdots , k_n\). Define the mean curvatures \(H_i\) of \(N\) by \(\prod_{i=1}^n(1+k_ix)=\sum_{i=1}^n\binom ni H_ix^i\). The author gives a sharp estimate for \(H_i\) in the case where \(M\) is a warped product of \(\mathbb{R}\) and a Ricci-flat manifold.