SOME ESTIMATES FOR COMPACT HYPERSURFACES IN HYPERBOLIC SPACE

ETEMAD, AZAM

doi:10.4134/BKMS.2005.42.1.039

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SOME ESTIMATES FOR COMPACT HYPERSURFACES IN HYPERBOLIC SPACE

Journal title : Bulletin of the Korean Mathematical Society
Volume 42, Issue 1, 2005, pp.39-44
Publisher : The Korean Mathematical Society
DOI : 10.4134/BKMS.2005.42.1.039

Title & Authors

SOME ESTIMATES FOR COMPACT HYPERSURFACES IN HYPERBOLIC SPACE
ETEMAD, AZAM;

Abstract

Let M be a compact hypersurface in hyperbolic space and let A be the area of M and V be the volume of the compact domain bounded by M. In this paper, we find a lower bound for ${$\frac{A}{V}$}$ in two cases, M has constant scalar curvature and M has constant mean curvature.

Keywords

scalar curvature;mean curvature;hyperbolic space;Riemannian manifold;

Language

English

Cited by

References

K. R. Frensel, Stable Complete Surfaces with Constant Mean Curvature, Bol. Soc. Brasil. Mat. (N.S.) 27 (1996), no. 2, 129-144

R. Reily, Applications of the Hessian operator in a Riemannian manifold, Indiana Univ. Math. J. 26 (1977), 459-472

S. T. Yau, Problem Section, Seminar on Differential Geometry, Ann. of Math. Stud. 102 (1982)