Helly's Intersection Theorem on Manifolds of Nonpositive Curvature
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.
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.