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

Xiaojun Huang; Wanke Yin

doi:10.1016/j.aim.2016.12.008

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

Xiaojun Huang, Wanke Yin

School of Arts and Sciences, Mathematics

Rutgers, The State University

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

This is the second article of the two papers, in which we investigate the holomorphic and formal flattening problem of a non-degenerate CR singular point of a codimension two real submanifold in Cⁿ with n≥3. The problem is motivated from the study of the complex Plateau problem that looks for the Levi-flat hypersurface bounded by a given real submanifold and by the classical complex analysis problem of finding the local hull of holomorphy of a real submanifold in a complex space. The present article is focused on non-degenerate flat CR singular points with at least one non-parabolic Bishop invariant. We will solve the formal flattening problem in this setting. The results in this paper and those in [23] are taken from our earlier arxiv post [22]. We split [22] into two independent articles to avoid it being too long.

Original language	American English
Pages (from-to)	1009-1073
Number of pages	65
Journal	Advances in Mathematics
Volume	308
DOIs	https://doi.org/10.1016/j.aim.2016.12.008
State	Published - Feb 21 2017

ASJC Scopus subject areas

General Mathematics

Keywords

Bishop invariants
CR singular points
Formal flattening
Integrability condition
Nonminimal CR points

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10.1016/j.aim.2016.12.008

Cite this

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abstract = "This is the second article of the two papers, in which we investigate the holomorphic and formal flattening problem of a non-degenerate CR singular point of a codimension two real submanifold in Cn with n≥3. The problem is motivated from the study of the complex Plateau problem that looks for the Levi-flat hypersurface bounded by a given real submanifold and by the classical complex analysis problem of finding the local hull of holomorphy of a real submanifold in a complex space. The present article is focused on non-degenerate flat CR singular points with at least one non-parabolic Bishop invariant. We will solve the formal flattening problem in this setting. The results in this paper and those in [23] are taken from our earlier arxiv post [22]. We split [22] into two independent articles to avoid it being too long.",

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KW - Integrability condition

KW - Nonminimal CR points

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

Abstract

ASJC Scopus subject areas

Keywords

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