Journal of Convex Analysis 13 (2006), No. 3, 785--798
Copyright Heldermann Verlag 2006
Helly's Intersection Theorem on Manifolds of Nonpositive Curvature
Yuri S. Ledyaev
Dept. of Mathematics, Western Michigan University, Kalamazoo, MI 49008, U.S.A.
Permanent Address: Steklov Insitute of Mathematics, 117966 Moscow, Russia
ledyaev@wmich.edu
Jay S. Treiman
Dept. of Mathematics, Western Michigan University, Kalamazoo, MI 49008, U.S.A.
jay.treiman@wmich.edu
Qiji J. Zhu
Dept. of Mathematics, Western Michigan University, Kalamazoo, MI 49008, U.S.A.
qiji.zhu@wmich.edu
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.
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