Minimal pseudo-Anosov translation lengths on the complex of curves

Let Sg,n be an orientable surface with genus g and n punctures. For simplicity, we shall drop the subscripts and denote it by S . The complex of curves C(S), is a locally infinite simplicial complex whose vertices are the isotopy classes of essential, non-peripheral, simple closed curves on S . A collection of vertices span a simplex if the curves can be isotoped to be disjoint or minimally intersecting on S . Here, we will assume that the surface S is non-sporadic i.e., the complexity ξ(S) = 3g − 3 + n > 2. For sporadic surfaces, the complex of curves C(S), is either trivial or well-understood.