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

Xiaojun Huang, Wanke Yin

Research output: Contribution to journalArticle

9 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 languageEnglish (US)
Pages (from-to)1009-1073
Number of pages65
JournalAdvances in Mathematics
Volume308
DOIs
StatePublished - Feb 21 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

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

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