Maximum principle for semi-elliptic trace operators and geometric applications

TL;DR

This paper develops a general maximum principle for trace operators and applies it to extend curvature estimates and a slice theorem in differential geometry.

Contribution

It introduces a broad weak maximum principle for trace operators and extends key geometric theorems using this new framework.

Findings

Established a generalized maximum principle for trace operators.

Extended higher order mean curvature estimates.

Generalized the Alias-Impera-Rigoli Slice Theorem.

Abstract

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