The subset of [formula omitted] realizing metrics on the curve complex.

For each point V , a subset of R 3 , we define a distance on the one skeleton of curve complex for each point and prove that (1) for each point in V with all positive entries, the one skeleton of curve complex under this distance is a metric space and δ -hyperbolic for some δ ∈ R + ; (2) for each point in V with at least one non-positive entry, the diameter of vertices of curve complex under this distance is finite. [ABSTRACT FROM AUTHOR]