Journal of the Mathematical Society of Japan

Complete non-compact spacelike hypersurfaces of constant mean curvature in de Sitter spaces

Sebastián MONTIEL

Full-text: Open access

Abstract

We use the half-space model for the open set of a de Sitter space associated to the steady state space to obtain some sharp a priori estimates for the height and the slope of certain constant mean curvature spacelike graphs. These estimates allow us to prove some existence and uniqueness theorems about complete non-compact constant mean curvature spacelike hypersurfaces in de Sitter spaces with prescribed asymptotic future boundary. Their geometric properties are studied.

Article information

Source
J. Math. Soc. Japan Volume 55, Number 4 (2003), 915-938.

Dates
First available in Project Euclid: 3 October 2007

Permanent link to this document
http://projecteuclid.org/euclid.jmsj/1191418756

Digital Object Identifier
doi:10.2969/jmsj/1191418756

Mathematical Reviews number (MathSciNet)
MR2003752

Zentralblatt MATH identifier
1049.53044

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42] 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42] 53C50: Lorentz manifolds, manifolds with indefinite metrics 35Q75: PDEs in connection with relativity and gravitational theory 83C99: None of the above, but in this section

Keywords
Constant mean curvature spacelike hypersurface de Sitter space

Citation

MONTIEL, Sebastián. Complete non-compact spacelike hypersurfaces of constant mean curvature in de Sitter spaces. J. Math. Soc. Japan 55 (2003), no. 4, 915--938. doi:10.2969/jmsj/1191418756. http://projecteuclid.org/euclid.jmsj/1191418756.


Export citation