
Journal of Convex Analysis 13 (2006), No. 3, 785798 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 R^{N} 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 Ndimensional CartanHadamard manifold contain a common point, then all sets from this family contain a common point. [ Fulltextpdf (351 KB)] for subscribers only. 