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

Part of: Global differential geometry

Published online by Cambridge University Press:  27 October 2014

Sandra C. García-Martínez ,
Debora Impera  and
Marco Rigoli
Sandra C. García-Martínez
Affiliation:
Instituto de Matemática e Estadística, Universidades de São Paulo, Rua do Matão 1010, Cidade Universitária, São Paulo, Brazil, ([email protected])
Debora Impera
Affiliation:
Dipartimento di Matematica e Applicazioni, Università degli studi di Milano Bicocca, via Cozzi 53, 20125 Milano, Italy, ([email protected])
Marco Rigoli
Affiliation:
Dipartimento di Matematica, Università degli studi di Milano, via Saldini 50, 20133 Milano, Italy, ([email protected])
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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 in a slice. We apply these results to draw topological conclusions at the end of the paper.

Keywords

height estimatesconstant mean curvaturehigher-order mean curvatureswarped products

MSC classification

Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 2 , June 2015 , pp. 403 - 419
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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