Let M be a metric space and P a finite set of points in M. The Steiner ratio in M is defined to be ρ(M)=inf{Ls(P)/Lm(P)•PℝM}, where Ls(P) and Lm(P) are the lengths of the Steiner minimal tree and the minimal spanning tree on P, respectively. In this paper, various conjectures on ρ(M) are studied. In particular, it is shown that for n-dimensional Euclidean space ℝn,ρ(ℝn)ℝ/b>q0.615.
