What this route deliberately avoids

Geometrization requires, in addition to everything above, the analysis of the long-time behaviour of the flow: the thick–thin decomposition, collapsing with local lower curvature bounds, and the recognition of graph manifolds — together with the JSJ decomposition and Thurston’s eight geometries on the topological side. None of that is needed here. Finite extinction short-circuits it: the flow simply ends, so its long-time behaviour never has to be described. Morgan–Tian say so explicitly — the argument “avoids all references to the nature of the flow as time goes to infinity” — and they defer geometrization to a second volume published seven years later.