  Based on ideas of L. Al\'ias, D. Impera and M. Rigoli developed in
"Hypersurfaces of constant higher order mean curvature in warped products", we
develope a fairly general weak/Omori-Yau maximum principle for trace operators.
We apply this version of maximum principle to generalize several higher order
mean curvature estimates and to give an extension of Alias-Impera-Rigoli Slice
Theorem
