Steinness of the Fatou set for a rational map of the complex projective   plane
  For a dominant algebraically stable rational self-map of the complex projective plane of degree at least 2, we will consider three different definitions of Fatou set and show the equivalence of them. Consequently, it follows that all Fatou components are Stein. This is an improvement of an early result by Fornaess and Sibony. 
Kazutoshi Maegawa