A Sharp Height Estimate for Compact Hypersurfaces with Constant k-Mean Curvature in Warped Product Spaces

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 in a slice. We apply these results to draw topological conclusions at the end of the paper.

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Bibliographic Details
Published inProceedings of the Edinburgh Mathematical Society Vol. 58; no. 2; pp. 403 - 419
Main Authors García-Martínez, Sandra C., Impera, Debora, Rigoli, Marco
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.06.2015
Subjects
Boundaries
Constants
Curvature
Estimates
Geometry
Graphs
Mathematical analysis
Mathematics
Studies
Topology
warped products
constant mean curvature
Primary 53C42
height estimates
higher-order mean curvatures
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Summary: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 in a slice. We apply these results to draw topological conclusions at the end of the paper.
Bibliography:ObjectType-Article-1
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ISSN:0013-0915
1464-3839
DOI:10.1017/S0013091514000157