A contractible Levi-flat hypersurface in C^2 which is a determining set for pluriharmonic functions
Complex Variables
2007-05-23 v3
Abstract
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.
Cite
@article{arxiv.math/0406572,
title = {A contractible Levi-flat hypersurface in C^2 which is a determining set for pluriharmonic functions},
author = {Franc Forstneric},
journal= {arXiv preprint arXiv:math/0406572},
year = {2007}
}
Comments
Arkiv Math., to appear