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arXiv · 1703.09135

Flattening a non-degenerate CR singular point of real codimension two

Hanlong Fang·Xiaojun Huang
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Abstract

This paper continues the previous studies in two papers of Huang-Yin [HY3-4] on the flattening problem of a CR singular point of real codimension two sitting in a submanifold in ${\mathbb C}^{n+1}$ with $n+1\ge 3$, whose CR points are non-minimal. Partially based on the geometric approach initiated in [HY3] and a formal theory approach used in [HY4], we are able to provide a very general flattening theorem for a non-degenerate CR singular point. As an application, we provide a solution to the local complex Plateau problem and obtain the analyticity of the local hull of holomorphy near a real analytic definite CR singular point in a general setting.

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Hanlong Fang, Xiaojun Huang. 2017-03-27. Flattening a non-degenerate CR singular point of real codimension two. https://arxiv.org/abs/1703.09135

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