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

Abstract

This paper continues the previous studies in two papers of Huang–Yin [HY16,HY17] 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 ≥ 3, whose CR points are non-minimal. Partially based on the geometric approach initiated in [HY16] and a formal theory approach used in [HY17], we are able to provide more or less a complete solution to the flattening problem for a non-degenerate CR singular point along the lines of such studies. 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.