Abstract

We give a generalization of the classical Helly's theorem on intersection of convex sets in RN\mathbb{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 N-dimensional Cartan-Hadamard manifold contain a common point, then all sets from this family contain a common point

Author information

Contact details are reproduced from the original publication and may be historical.

Yuri S. Ledyaev

Dept. of Mathematics, Western Michigan University, Kalamazoo, MI 49008, U.S.A.
Permanent Address: Steklov Institute 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

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Suggested citation

Y. S. Ledyaev, J. S. Treiman, Q. J. Zhu. “Helly's Intersection Theorem on Manifolds of Nonpositive Curvature.” Journal of Convex Analysis 13 (2006), No. 3/4, 785–798. https://doi.org/10.68381/jca13059

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Published by Heldermann Verlag, 2006. Rights now held by Banach Press LLC.