Construction of an acylindrical hyperbolic 3-manifold with quasi-Fuchsian boundary

One way to obtain a Kleinian group is to consider the group generated by reflections in the faces of a hyperbolic polyhedron with dihedral angles submultiples of \pi. Andreev’s theorem guarantees the existence of hyperbolic polyhedra with non-obtuse dihedral angles satisfying certain combinatorial conditions. In this talk, I will construct a one dimensional family of hyperbolic polyhedra with the help of Andreev’s theorem, so that the Kleinian groups generated by reflections in some of the faces realize a one dimensional deformation of a convex cocompact acylindrical hyperbolic 3-manifold.