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

2017/03/27 by Hanlong Fang, Fang, Hanlong, Huang, Xiaojun
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1703.09135

openalex publication_date 2017/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Cⁿ⁺¹ with n+1≥ 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.

Related

• Flattening of CR singular points and analyticity of local hull of holomorphy
• On removable singularities for CR functions in higher codimension
• Real submanifolds of maximum complex tangent space at a CR singular point, II
• CR singularities of real fourfolds in ℂ³
• CR functions at CR singularities: approximation, extension, and hulls