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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hypersurfaces of constant higher order mean curvature in warped products


Authors: Luis J. Alías, Debora Impera and Marco Rigoli
Journal: Trans. Amer. Math. Soc. 365 (2013), 591-621
MSC (2010): Primary 53C40, 53C42, 53A10
Published electronically: September 12, 2012
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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.


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Additional Information

Luis J. Alías
Affiliation: Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Espinardo, Murcia, Spain
Email: ljalias@um.es

Debora Impera
Affiliation: Dipartimento di Matematica, Università degli studi di Milano, via Saldini 50, I-20133 Milano, Italy
Email: debora.impera@unimi.it

Marco Rigoli
Affiliation: Dipartimento di Matematica, Università degli studi di Milano, via Saldini 50, I-20133 Milano, Italy
Email: marco.rigoli@unimi.it

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05774-6
PII: S 0002-9947(2012)05774-6
Received by editor(s): January 11, 2011
Published electronically: September 12, 2012
Additional Notes: The first author was partially supported by MICINN project MTM2009-10418 and Fundación Séneca project 04540/GERM/06, Spain. This research is a result of the activity developed within the framework of the Programme in Support of Excellence Groups of the Región de Murcia, Spain, by Fundación Séneca, Regional Agency for Science and Technology (Regional Plan for Science and Technology 2007-2010).
The third author was partially supported by MEC Grant SAB2010-0073
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.