Let $ M $ be a complete hyperbolic 3-manifold admitting a homotopy equivalence to a compact surface $ \Sigma $, such that the cusps of $ M $ are in bijective correspondence with the boundary components of $ \Sigma $. Suppose we realise a tight geodesic in the curve complex as a sequence of closed geodesics $ M $. There is an upper bound on the lengths of such curves in terms of the lengths of the terminal curves and the topologicial type of $ \Sigma $. We give proofs of these and related bounds. Similar bounds have been proven by Minsky using the sophisticated machinery of hierarchies. Such bounds feature in the work of Brock, Canary and Minsky towards the ending lamination conjecture, and can also be used to study the action of the mapping class group on the curve complex.
Geom. Funct. Anal. 17 (2007) 1001-1042.