A sharp height estimate for compact hypersurfaces with constant $k$-mean curvature in 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.

19 pages. To appear on Proceedings of the Edinburgh Mathematical Society