On deformations of hyperbolic 3-manifolds with geodesic boundary (Q2492036)

Let \(M\) be a complete finite-volume hyperbolic 3-manifold with compact non-empty geodesic boundary and let \(\mathcal T\) be a geometric partially truncated triangulation of \(M\) [see \textit{R. Frigerio} and \textit{C. Petronio}, Trans. Am. Math. Soc. 356, No.~8, 3243--3282 (2004; Zbl 1052.57018)]. Assume that \(M\) has \(k\) toric cusps. The author shows that the set of solutions of consistency equations for \(T\) is a smooth manifold of real dimension \(2k\) near the point representing a unique complete structure on \(M\), and gives some applications of the result.