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Constant Mean Curvature Hypersurfaces in the Steady State Space: A Survey

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Lorentzian Geometry and Related Topics (GELOMA 2016)

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Abstract

In this survey, we review recent progress in the theory of spacelike hypersurfaces with constant mean curvature in the steady state space. Using the different models of this space, we outline the major concepts, techniques, and results with a special focus on Bernstein-type theorems, hypersurfaces with boundary in a slice, and the Dirichlet problem for the constant mean curvature equation.

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Acknowledgements

The author has been partially supported by the MINECO/FEDER grant MTM2014-52368-P.

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Authors and Affiliations

  1. Departamento de Geometría y Topología, Instituto de Matemáticas (IEMath-GR), Universidad de Granada, 18071, Granada, Spain

    Rafael López

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  1. Rafael López
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Correspondence to Rafael López .

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Editors and Affiliations

  1. Department of Algebra, Geometry, Topology, University of Malaga, Málaga, Spain

    María A. Cañadas-Pinedo

  2. Department of Algebra, Geometry, Topology, University of Malaga, Málaga, Spain

    José Luis Flores

  3. Department of Applied Mathematics, University of Malaga, Malaga, Spain

    Francisco J. Palomo

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López, R. (2017). Constant Mean Curvature Hypersurfaces in the Steady State Space: A Survey. In: Cañadas-Pinedo, M., Flores, J., Palomo, F. (eds) Lorentzian Geometry and Related Topics. GELOMA 2016. Springer Proceedings in Mathematics & Statistics, vol 211. Springer, Cham. https://doi.org/10.1007/978-3-319-66290-9_11

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