A contractible Levi-flat hypersurface in C2 which is a determining set for pluriharmonic functions
Abstract
We construct a real analytic Levi-flat hypersurface M in a neighborhood of an ellipsoid B in C2 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 R3 and has a basis of Stein neighborhoods in C2, (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.
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