Geodesic
Helly's Intersection Theorem on Manifolds of Nonpositive Curvature
Journal of convex analysis, Tome 13 (2006) no. 3, pp. 785-798.

Voir la notice de l'article provenant de la source Heldermann Verlag

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. 
@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},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2006},
     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
PB  - mathdoc
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
%I mathdoc
%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
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/