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arXiv · 1210.5146

Flattening of CR singular points and analyticity of local hull of holomorphy

Xiaojun Huang·Wanke Yin
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Abstract

A primary goal in this paper is to study the question that asks when a real analytic submanifold $M$ in ${\mathbb{C}}^{n+1}$ bounds a real analytic (up to $M$) Levi-flat hypersurface $\hat{M}$ near $p\in M$ such that $\hat{M}$ is foliated by a family of complex hypersurfaces moving along the normal direction of $M$ at $p$, and gives the invariant local hull of holomorphy of $M$ near $p$. This question is equivalent to the holomorphic flattening problem for $M$ near $p$. We will give an affirmative answer to above question when $p$ is a real complex tangent point with at least one elliptic direction (positively curved direction). We also obtain a formal flattening theorem under the assumption of one non-parabolic direction.

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Xiaojun Huang, Wanke Yin. 2012-10-18. Flattening of CR singular points and analyticity of local hull of holomorphy. https://arxiv.org/abs/1210.5146

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