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On the total curvature of convex hypersurfaces in hyperbolic spaces


Author: Albert Borbély
Journal: Proc. Amer. Math. Soc. 130 (2002), 849-854
MSC (1991): Primary 53C21
DOI: https://doi.org/10.1090/S0002-9939-01-06101-9
Published electronically: October 5, 2001
MathSciNet review: 1866041
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $C_{1}\subset C_{2}\subset H^{n}$ be two convex compact subsets of the hyperbolic space $H^{n}$ with smooth boundary. It is shown that the total curvature of the hypersurface $\partial C_{2}$ is larger than the total curvature of $\partial C_{1}$.


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

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  • 2. Chern, S-S., On the curvatura integra in a Riemannian manifold, Annals of Math. 46 (1945), 674-684. MR 7:328c
  • 3. Croke, C., A sharp four dimensional isoperimetric inequality, Comment. Math. Helv. 59 (1984), 187-192. MR 85f:53060
  • 4. Kleiner, B., An isoperimetric comparison theorem, Invent. Math. 108 (1992), 37-47. MR 92m:53056

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Additional Information

Albert Borbély
Affiliation: Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
Email: borbely@mcs.sci.kuniv.edu.kw

DOI: https://doi.org/10.1090/S0002-9939-01-06101-9
Keywords: Total curvature, Gauss-Kronecker curvature, isoperimetric inequality
Received by editor(s): February 15, 2000
Received by editor(s) in revised form: September 20, 2000
Published electronically: October 5, 2001
Additional Notes: This research was supported by the Kuwait University Research Grant SM 03/99
Communicated by: Wolfgang Ziller
Article copyright: © Copyright 2001 American Mathematical Society

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