Description
Holonomy groups of complete hyperbolic structures on 3-manifolds are discrete subgroups of $\mathrm{PSL}(2,\mathbb{C})$. This means that the deformation space of complete hyperbolic structures can be embedded as an open subset of a representation variety. If multiple such deformation spaces live in the same character variety, how are they related to each other? One way to understand this is to deform the hyperbolic metric through incomplete metrics, either by hand or by an abstract harmonic theory due to Hodgson--Kerckhoff. As an application, we prove a conjecture of Lee and Sakuma, that there is a continuous path of hyperbolic cone 3-manifolds joining any hyperbolic 2-bridge knots to the boundary of a Teichmuller space, for knots that are highly twisted in a precise sense.