Convex domains with locally Levi-flat boundaries
Complex Variables
2012-02-17 v3
Abstract
It is shown that a domain in which is locally convex and has -smooth Levi-flat boundary is locally linearly equivalent to a Cartesian product of a planar domain and This result does not extend to the case where the Levi form has locally constant rank for some .
Keywords
Cite
@article{arxiv.1112.1867,
title = {Convex domains with locally Levi-flat boundaries},
author = {Nikolai Nikolov and Pascal J. Thomas},
journal= {arXiv preprint arXiv:1112.1867},
year = {2012}
}
Comments
We learned that the main result of the paper is a special case of the result by V. K. Beloshapka and S. N. Bychkov in "A property of convex hypersurfaces in C^n", Mat. Zametki 40 (1986), no. 5. Interested readers should refer to that work