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Space-like hypersurfaces with functionally bounded mean curvature in Lorentzian warped products and generalized Calabi–Bernstein-type problems

Part of: Global differential geometry Elliptic equations and systems

Published online by Cambridge University Press:  22 June 2018

Juan A. Aledo ,
Rafael M. Rubio  and
Juan J. Salamanca
Juan A. Aledo
Affiliation:
Departamento de Matemáticas, Escuela Superior de Informática, Universidad de Castilla-La Mancha, 02071 Albacete, Spain (juanangel.aledo@uclm.es)
Rafael M. Rubio
Affiliation:
Departamento de Matemáticas, Campus de Rabanales, Universidad de Córdoba, 14071 Córdoba, Spain (rmrubio@uco.es; jjsalamanca@uco.es)
Juan J. Salamanca
Affiliation:
Departamento de Matemáticas, Campus de Rabanales, Universidad de Córdoba, 14071 Córdoba, Spain (rmrubio@uco.es; jjsalamanca@uco.es)
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Abstract

We study space-like hypersurfaces with functionally bounded mean curvature in Lorentzian warped products , where F is a (non-compact) complete Riemannian manifold whose universal covering is parabolic. In particular, we provide several rigidity results under appropriate mathematical and physical assumptions. As an application, several Calabi–Bernstein-type results are obtained which widely extend the previous ones in this setting.

Keywords

Lorentzian warped productsspace-like hypersurfacesmean curvatureparabolicityCalabi–Bernstein problems

MSC classification

Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
Secondary: 35J60: Nonlinear elliptic equations 53C50: Lorentz manifolds, manifolds with indefinite metrics
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 4 , August 2019 , pp. 849 - 868
Copyright
Copyright © Royal Society of Edinburgh 2018 

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Footnotes

Dedicated to to Professor Alfonso Romero on the occasion of his 60th birthday

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