Helly's Intersection Theorem on Manifolds of Nonpositive Curvature

Authors

Yuri S. Ledyaev, Western Michigan University
Jay S. Treiman, Western Michigan University
Qiji Jim Zhu, Western Michigan UniversityFollow

Document Type

Article

Publication Date

2006

Abstract

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 N-dimensional Cartan-Hadamard manifold contain a common point, then all sets from this family contain a common point.

WMU ScholarWorks Citation

Ledyaev, Yuri S.; Treiman, Jay S.; and Zhu, Qiji Jim, "Helly's Intersection Theorem on Manifolds of Nonpositive Curvature" (2006). Math Faculty Publications. 33.
https://scholarworks.wmich.edu/math_pubs/33