The subset of R3R3 realizing metrics on the curve complex

For each point VV, a subset of R3R3, we define a distance on the one skeleton of curve complex for each point and prove that (1) for each point in VV with all positive entries, the one skeleton of curve complex under this distance is a metric space and δ  -hyperbolic for some δ∈R+δ∈R+; (2) for each point in VV with at least one non-positive entry, the diameter of vertices of curve complex under this distance is finite.