In this paper, we develop a series of general integral formulae for compact spacelike hypersurfaces with hyperplanar boundary in the (n + 1)-dimensional Minkowski space-time L n+1 . As an application of them, we prove that the only compact spacelike hypersurfaces in L n+1 having constant higher orde
Spacelike constant mean curvature surfaces in pseudo-Riemannian space forms
β Scribed by Bennett Palmer
- Publisher
- Springer
- Year
- 1990
- Tongue
- English
- Weight
- 343 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0232-704X
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π SIMILAR VOLUMES
We study compact spacelike hypersurfaces (necessarily with non-empty boundary) with constant mean curvature in the (n + 1)-dimensional Lorentz-Minkowski space. In particular, when the boundary is a round sphere we prove that the only such hypersurfaces are the hyperplanar round balls (with zero mean
It is shown that a compact spacelike hypersurface which is contained in the chronological future (or past) of an equator of de Sitter space is a totally umbilical round sphere if one of the mean curvatures H l does not vanish and the ratio H k /H l is constant for some k, l, 1 β€ l < k β€ n. This exte