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Some results on the convex hull of finitely many convex sets
Author(s):
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  points on Hadamard manifolds with pinched curvature. It was known previously that the volume is bounded by some polynomial in  . The estimate comes from the study of the convex hull of finitely many convex sets on Hadamard manifolds.
References:
- [ANC]
- A. Ancona, Convexity at infinity and Brownian motion on manifolds with unbounded negative curvature, Rev. Mat. Iberoamericana 10 (1994), 189-220. MR 95a:58132
- [AN]
- M.T. Anderson, The Dirichlet problem at infinity for manifolds of negative curvature, J. Differential Geometry 18 (1983), 701-721. MR 85m:58178
- [BO1]
- A. Borbély, A note on the Dirichlet problem at infinity for manifolds of negative curvature, Proc. Amer. Math. Soc. 114 (1992), 865-872. MR 92f:58180
- [BO2]
- A. Borbély, The nonsolvability of the Dirichlet Problem on negatively curved manifolds, Differ. Geom. and Appl., to appear.
- [BOW]
- B.H. Bowditch, Some results on the geometry of convex hulls in manifolds of pinched negative curvature, Comment. Math. Helvetici 69 (1994), 49-81. MR 94m:53044
- [BOW1]
- B.H. Bowditch, Geometrical finiteness with variable negative curvature, Preprint, I.H.E.S. (1990).
- [CHA]
- I. Chavel, Riemannian Geometry - A modern introduction, Cambridge University Press (1993). MR 95j:53001
- [CH]
- Choi, H. I., Asymptotic Dirichlet problems for harmonic functions on Riemannian manifolds, Trans. Amer. Math. Soc. 281 (1984), 691-716. MR 85b:53040
- [EO]
- P. Eberlain, B. O'Neill, Visibility manifolds, Pacific J. Math 46 (1973), 45-109.
- [GW]
- R.E.Greene, H. Wu,
 Approximations of convex, subharmonic and plurisubharmonic functions, Ann. Sci. École Norm. Sup. 12 (1979), 69-100. MR 80m:53055 - [HK]
- E. Heintze, H. Karcher, A general comparison theorem with applications to volume estimates for submanifolds, Ann. Sci. Éc. Norm. Sup., Paris 11 (1978), 451-470. MR 80i:53026
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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:
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
Copyright of article:
Copyright
1998,
American Mathematical Society
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