In this paper we find the
formula for the pluricomplex Green function of the unit ball of ℂn with two poles of
equal weights. The strategy will be to show the existence of a foliation of the ball
(singular at the poles) by proper smooth analytic discs passing through one or
through both of the poles, such that the restriction of the pluricomplex Green
function to these discs is harmonic away from the poles. This foliation is
obtained by solving a suitable extremal problem, in analogy to the results of
Lempert in the case of one pole for convex domains. Using the expression of the
Green function along each leaf of the foliation, we construct its formula on
the whole ball. We then show that this function is of class C1,1 but not
C2.
