Journal of convex analysis, Tome 13 (2006) no. 3, pp. 785-798
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Y. S. Ledyaev; J. S. Treiman; Q. J. Zhu. Helly's Intersection Theorem on Manifolds of Nonpositive Curvature. Journal of convex analysis, Tome 13 (2006) no. 3, pp. 785-798. http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a19/
@article{JCA_2006_13_3_JCA_2006_13_3_a19,
author = {Y. S. Ledyaev and J. S. Treiman and Q. J. Zhu},
title = {Helly's {Intersection} {Theorem} on {Manifolds} of {Nonpositive} {Curvature}},
journal = {Journal of convex analysis},
pages = {785--798},
year = {2006},
volume = {13},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a19/}
}
TY - JOUR
AU - Y. S. Ledyaev
AU - J. S. Treiman
AU - Q. J. Zhu
TI - Helly's Intersection Theorem on Manifolds of Nonpositive Curvature
JO - Journal of convex analysis
PY - 2006
SP - 785
EP - 798
VL - 13
IS - 3
UR - http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a19/
ID - JCA_2006_13_3_JCA_2006_13_3_a19
ER -
%0 Journal Article
%A Y. S. Ledyaev
%A J. S. Treiman
%A Q. J. Zhu
%T Helly's Intersection Theorem on Manifolds of Nonpositive Curvature
%J Journal of convex analysis
%D 2006
%P 785-798
%V 13
%N 3
%U http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a19/
%F JCA_2006_13_3_JCA_2006_13_3_a19
We give a generalization of the classical Helly's theorem on intersection of convex sets in RN for the case of manifolds of nonpositive curvature. In particular, we show that if any N+1 sets from a family of closed convex sets on N-dimensional Cartan-Hadamard manifold contain a common point, then all sets from this family contain a common point.
