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arXiv · 1112.1867

Convex domains with locally Levi-flat boundaries

Nikolai Nikolov·Pascal J. Thomas
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Abstract

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 $k<n-1$.

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Nikolai Nikolov, Pascal J. Thomas. 2012-02-16. Convex domains with locally Levi-flat boundaries. https://arxiv.org/abs/1112.1867

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