A sharp height estimate for compact hypersurfaces with constant $k$-mean curvature in warped product spaces

TL;DR

This paper derives a precise height estimate for compact hypersurfaces with constant higher order mean curvature in warped product spaces, leading to topological insights.

Contribution

It provides a new sharp height estimate for such hypersurfaces with boundary in a slice within warped product spaces, extending previous geometric bounds.

Findings

Established a sharp height bound for hypersurfaces with constant k-mean curvature

Derived topological consequences from the height estimates

Applied the results to specific classes of warped product spaces

Abstract

In this paper we obtain a sharp height estimate concerning compact hypersurfaces immersed into warped product spaces with some constant higher order mean curvature, and whose boundary is contained into a slice. We apply these results to draw topological conclusions at the end of the paper.