%0 Journal Article %T Maximum principle for semi-elliptic trace operators and geometric applications %A G. Pacelli Bessa %A Leandro F. Pessoa %J Mathematics %D 2012 %I arXiv %X 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 %U http://arxiv.org/abs/1208.1322v1