Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the volume and the Gauss map image of spacelike hypersurfaces in de Sitter space


Authors: Juan A. Aledo and Luis J. Alías
Journal: Proc. Amer. Math. Soc. 130 (2002), 1145-1151
MSC (2000): Primary 53C42; Secondary 53B30, 53C50
Published electronically: September 19, 2001
MathSciNet review: 1873790
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we prove that a complete spacelike hypersurface $M^n$ in de Sitter space such that its image under the Gauss map is contained in a hyperbolic geodesic ball of radius $\varrho$is necessarily compact and its $n$-dimensional volume satisfies $\omega_n/\mathrm{cosh}(\varrho)\leq \mathrm{vol}(M)\leq\omega_n\mathrm{ cosh}^{n}(\varrho)$, where $\omega_n$ denotes the volume of a unitary round $n$-sphere. We also characterize the case where these inequalities become equalities. As an application of our result, we also conclude that Goddard's conjecture is true under the assumption that the hyperbolic image of the hypersurface is bounded.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53C42, 53B30, 53C50

Retrieve articles in all journals with MSC (2000): 53C42, 53B30, 53C50


Additional Information

Juan A. Aledo
Affiliation: Departamento de Matemáticas, Universidad de Castilla-La Mancha, Escuela Politécnica Superior de Albacete, 02071 Albacete, Spain
Email: jaledo@pol-ab.uclm.es

Luis J. Alías
Affiliation: Departamento de Matemáticas, Universidad de Murcia, 30100 Espinardo, Murcia, Spain
Email: ljalias@um.es

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06133-0
PII: S 0002-9939(01)06133-0
Keywords: de Sitter space, spacelike hypersurface, volume, Gauss map, hyperbolic image, mean curvature
Received by editor(s): April 17, 2000
Received by editor(s) in revised form: October 5, 2000
Published electronically: September 19, 2001
Additional Notes: This work has been partially supported by DGICYT Grant No PB97-0784-C03-02 and Consejería de Educación y Cultura CARM, Programa Séneca (PRIDTYC)
Communicated by: Wolfgang Ziller
Article copyright: © Copyright 2001 American Mathematical Society