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/