Abstract
In this paper we prove an integral inequality for the Gaussian curvature of compact maximal surfaces inn-dimensional de Sitter space. Some applications of that inequality are given in order to solve the associated Bernstein type problem as well as to characterize the totally geodesic immersion in terms of its area and the first nontrivial eigenvalue of its Laplacian.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hersch, J.: Quatre propriétés isopérimétriques de membranes sphériques homogénes.C. R. Acad. Sc., Paris 270 (1970), 1645–1648.
Palmer, B.: The conformal Gauss map and the stability of Willmore surfaces.Ann. Global Anal. Geom. 9 (1991), 305–317.
Pinkall, U.: Hopf tori in S3.Invent. Math. 81 (1985), 379–386.
Author information
Authors and Affiliations
Additional information
Partially supported by a DGICYT Grant No. PB91-0705-C02-02
Partially supported by a DGICYT Grant No. PB91-0731
Rights and permissions
About this article
Cite this article
Alías, L.J., Romero, A. An integral inequality for compact maximal surfaces inn-dimensional de Sitter space and its applications. Ann Glob Anal Geom 13, 3–8 (1995). https://doi.org/10.1007/BF00774561
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00774561