Hypersurfaces of constant higher order mean curvature in warped products

TL;DR

This paper characterizes hypersurfaces with constant higher order mean curvature in warped product spaces using a novel trace operator version of the Omori-Yau maximum principle, advancing geometric analysis techniques.

Contribution

It introduces a new trace operator version of the Omori-Yau maximum principle for studying hypersurfaces with constant higher order mean curvature.

Findings

Characterization of compact hypersurfaces with constant higher order mean curvature.

Extension of maximum principle techniques to warped product spaces.

New analytical tools for geometric analysis in curved spaces.

Abstract

In this paper we characterize compact and complete hypersurfaces with some constant higher order mean curvature into warped product spaces. Our approach is based on the use of a new trace operator version of the Omori-Yau maximum principle which seems to be interesting in its own.