Translator Disclaimer
VOL. 1 | 2000 Constant Curvature Spacelike Hypersurfaces in the Lorentz–Minkowski Space
Luis J. Alias, Jose A. Pastor

Editor(s) Ivaïlo M. Mladenov, Gregory L. Naber

Abstract

In this paper we will report on some of our recent results about compact spacelike hypersurfaces with spherical boundary in the Lorentz–Minkowski space $\mathbb{L}^{n+1}$. In particular we will prove that the only compact spacelike hypersurfaces in $\mathbb{L}^{n+1}$ with constant mean curvature and spherical boundary are the hyperplanar balls and the hyperbolic caps. As for the case of the scalar curvature, we will prove that the only compact spacelike hypersurfaces in $\mathbb{L}^{n+1}$ with nonzero constant scalar curvature and spherical boundary are the hyperbolic caps. Our approach is based on the use of several integral formulas, among them there are a volume formula and a flux formula.

Information

Published: 1 January 2000
First available in Project Euclid: 5 June 2015

zbMATH: 1009.53061
MathSciNet: MR1884840

Digital Object Identifier: 10.7546/giq-1-2000-17-26

Rights: Copyright © 2000 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

PROCEEDINGS ARTICLE
10 PAGES


SHARE
Back to Top