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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some results on the convex hull
of finitely many convex sets


Author: Albert Borbély
Journal: Proc. Amer. Math. Soc. 126 (1998), 1515-1525
MSC (1991): Primary 53C20
MathSciNet review: 1425113
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Abstract: A better than quadratic estimate is given for the volume of the convex hull of $n$ points on Hadamard manifolds with pinched curvature. It was known previously that the volume is bounded by some polynomial in $n$. The estimate comes from the study of the convex hull of finitely many convex sets on Hadamard manifolds.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04155-0
PII: S 0002-9939(98)04155-0
Keywords: Convex hull
Received by editor(s): February 27, 1996
Received by editor(s) in revised form: October 14, 1996
Additional Notes: This was research supported by the Kuwait University Research Grant SM 146
Communicated by: Christopher Croke
Article copyright: © Copyright 1998 American Mathematical Society