Ampleness of canonical divisors of hyperbolic normal projective   varieties
  Let X be a projective variety which is algebraic Lang hyperbolic. We show that Lang's conjecture holds (one direction only): X and all its subvarieties are of general type and the canonical divisor K_X is ample at smooth points and Kawamata log terminal points of X, provided that K_X is Q-Cartier, no Calabi-Yau variety is algebraic Lang hyperbolic and a weak abundance conjecture holds. 
Fei Hu, Sheng Meng and De-Qi Zhang
math.AG math.CV math.DG