On the global rigidity of sphere packings on 3-dimensional manifolds
  In this paper, we prove the global rigidity of sphere packings on 3-dimensional manifolds. This is a 3-dimensional analogue of the rigidity theorem of Andreev-Thurston and was conjectured by Cooper and Rivin. We also prove a global rigidity result using a combinatorial scalar curvature introduced by Ge and the author. 
Xu Xu
math.GT math.DG