  We construct a real analytic Levi-flat hypersurface M in a neighborhood of an
ellipsoid B in C^2 such that the each leaf of the Levi foliation of M is a
complex disc, M intersects the boundary of B transversely, and the intersection
A of M with B has the following properties: (i) the closure of A is
diffeomorphic to the ball in R^3 and has a basis of Stein neighborhoods in C^2,
(ii) any real analytic function on A which is constant on each Levi leaf is
constant, (iii) any pluriharmonic function in a connected open neighborhood of
A and vanishing on A is identically zero.
