𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Constant mean curvature spacelike hypersurfaces with spherical boundary in the Lorentz-Minkowski space

✍ Scribed by Luis J. Alías; JoséA. Pastor

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
502 KB
Volume
28
Category
Article
ISSN
0393-0440

No coin nor oath required. For personal study only.

✦ Synopsis

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 curvature) and the hyperbolic caps (with non-zero constant mean curvature).

📜 SIMILAR VOLUMES

Spacelike hypersurfaces with constant hi
Spacelike hypersurfaces with constant higher order mean curvature in Minkowski space–time
✍ Luis J. Alías; J. Miguel Malacarne 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 115 KB

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

Remarks on compact spacelike hypersurfac
Remarks on compact spacelike hypersurfaces in de Sitter space with constant higher order mean curvature
✍ Luis J. Alı́as; Sung-Eun Koh 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 60 KB

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 ≤ l < k ≤ n. This exte