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An estimate for the total mean curvature in negatively curved spaces

Published online by Cambridge University Press:  17 April 2009

Albert Borbély
Albert Borbély
Affiliation:
Kuwait University, Department of Mathematics and Computer Science, P.O. Box 5969, Safat 13060Kuwait e-mail: borbely@ mcs.sci.kuniv.edu.kw
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Let Mn be a nonpositively curved complete simply connected manifold and D ⊂ Mn be a convex compact subset with non-empty interior and smooth boundary. It is shown that the total mean curvature ∂D can be estimated in terms of volume and curvature bound.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 66 , Issue 2 , October 2002 , pp. 267 - 273
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Borbély, A., ‘On the total curvature of convex hypersurfaces in hyperbolic spaces’, Proc. Amer. Math. Soc. (to appear).Google Scholar
[2]Chern, S-S., ‘On the curvatura integra in a Riemannian manifold’, Ann. of Math. 46 (1945), 674–684.CrossRefGoogle Scholar
[3]Kleiner, B., ‘An isoperimetric comparison theorem’, Invent. Math. 108 (1992), 37–47.CrossRefGoogle Scholar