Higher order mean curvature estimates for properly immersed \(\phi _{h}\)-bounded hypersurfaces (Q667347)

The authors obtain estimates on the higher mean curvatures of a properly and isometrically immersed $\phi_h$-bounded hypersurface $M$ in a product $N\times L$ of complete Riemannian manifolds. The estimates depend only on the geometry of $N$ and $L$. The notion of a $\phi_h$-bounded hypersurface in a product manifold was originally defined by the first two authors and \textit{B. P. Lima} in [Ann. Mat. Pura Appl. (4) 194, No. 1, 109--130 (2015; Zbl 1308.53079)]. Such hypersurfaces include all properly immersed cylindrically bounded hypersurfaces in $N\times L$.