Angle structures and hyperbolic $3$-manifolds with totally geodesic   boundary
  This notes explores angle structures on ideally triangulated compact $3$-manifolds with high genus boundary. We show that the existence of angle structures implies the existence of a hyperbolic metric with totally geodesic boundary, and conversely each hyperbolic $3$-manifold with totally geodesic boundary has an ideal triangulation that admits angle structures. 
Faze Zhang, Ruifeng Qiu and Tian Yang
math.GT