Bulletin of the Belgian Mathematical Society - Simon Stevin

Sharp height estimate in Lorentz-Minkowski space revisited

Eudes L. de Lima, Henrique F. de Lima, and Cícero P. Aquino

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Abstract

In this paper, we deal with compact (necessarily with nonempty boundary) generalized linear Weingarten spacelike hypersurfaces immersed into the Lorentz-Minkowski space $\mathbb L^{n+1}$, which means that there exists a linear relation involving some of the corresponding higher order mean curvatures. In this setting, we obtain a sharp height estimate concerning such a hypersurfaces whose boundary is contained in a spacelike hyperplane of $\mathbb L^{n+1}$. Furthermore, we apply our estimate to describe the nature of the end of a complete generalized linear Weingarten spacelike hypersurface in $\mathbb L^{n+1}$.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 25, Number 1 (2018), 29-38.

Dates
First available in Project Euclid: 11 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1523412050

Digital Object Identifier
doi:10.36045/bbms/1523412050

Mathematical Reviews number (MathSciNet)
MR3784503

Zentralblatt MATH identifier
06882539

Subjects
Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Secondary: 53B30: Lorentz metrics, indefinite metrics 53C50: Lorentz manifolds, manifolds with indefinite metrics

Keywords
Lorentz-Minkowski space higher order mean curvatures generalized linear Weingarten spacelike hypersurfaces height estimate

Citation

de Lima, Eudes L.; de Lima, Henrique F.; Aquino, Cícero P. Sharp height estimate in Lorentz-Minkowski space revisited. Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 1, 29--38. doi:10.36045/bbms/1523412050. https://projecteuclid.org/euclid.bbms/1523412050


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