Convex domains with locally Levi-flat boundaries

Details Convex domains with locally Levi-flat boundaries Convex domains with locally Levi-flat boundaries

2011-12-08

arxiv.org/abs/1112.1867v3

Mathematics

Complex Variables

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 prope

Scientific paper

It is shown that a domain in $\C^n$ which is locally convex and has $\mathcal
C^1$-smooth Levi-flat boundary is locally linearly equivalent to a Cartesian
product of a planar domain and $\C^{n-1}.$ This result does not extend to the
case where the Levi form has locally constant rank for some $k

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