Minimum volume cusped hyperbolic three-manifolds

This paper is the second in a series whose goal is to understand the structure of low-volume complete orientable hyperbolic $3$-manifolds. Using Mom technology, we prove that any one-cusped hyperbolic $3$-manifold with volume $\le 2.848$ can be obtained by a Dehn filling on one of $21$ cusped hyperbolic $3$-manifolds. We also show how this result can be used to construct a complete list of all one-cusped hyperbolic $3$-manifolds with volume $\le 2.848$ and all closed hyperbolic $3$-manifolds with volume $\le 0.943$. In particular, the Weeks manifold is the unique smallest volume closed orientable hyperbolic $3$-manifold.