Geometrical Finiteness, Holography, and the BTZ Black Hole
  We show how a theorem of Sullivan provides a precise mathematical statement of a 3d holographic principle, that is, the hyperbolic structure of a certain class of 3d manifolds is completely determined in terms of the corresponding Teichmuller space of the boundary. We explore the consequences of this theorem in the context of the Euclidean BTZ black hole in three dimensions. 
Danny Birmingham, Conall Kennedy, Siddhartha Sen, and Andy Wilkins