On the generalization of Forelli's theorem
  The purpose of this paper is to present a solution to perhaps the final remaining case in the line of study concerning the generalization of Forelli's theorem on the complex analyticity of the functions that are: (1) $\mathcal{C}^\infty$ smooth at a point, and (2) holomorphic along the complex integral curves generated by a contracting holomorphic vector field with an isolated zero at the same point. 
Jae-Cheon Joo, Kang-Tae Kim, Gerd Schmalz
math.CV