A non-compact convex hull in generalized non-positive curvature (Q6634478)

It is an open question of \textit{M. Gromov} [Geometric group theory. Volume 2: Asymptotic invariants of infinite groups. Proceedings of the symposium held at the Sussex University, Brighton, July 14-19, 1991. Cambridge: Cambridge University Press (1993; Zbl 0841.20039)] as to whether the closed convex hull of a compact subset of a complete CAT(0) space is compact. The authors of this paper show that if the CAT(0) condition is weakened to being a metric space with a conical bicombing, then the answer is no. They accomplish this by constructing a metric space with a conical bicombing that admits a finite subset whose closed convex hull in not compact. It should be noted that every CAT(0) space admits a unique conical bicombing.