Infinitesimal generators and the Loewner equation on complete hyperbolic   manifolds
  We characterize infinitesimal generators on complete hyperbolic complex manifolds without any regularity assumption on the Kobayashi distance. This allows to prove a general Loewner type equation with regularity of any order $d\in [1,+\infty ]$. Finally, based on these results, we focus on some open problems naturally arising. 
Leandro Arosio, Filippo Bracci
math.CV