Geometric and analytic problems for a real submanifold in ℂn with CR singularities

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In this survey article, we present some known results and also propose some open questions related to the analytic and geometric aspects of Bishop submanifolds in a complex space. We mainly focus on those problems that the author and his coauthors have recently worked on. The article also contains an example of a Bishop submanifold in ℂ3 of real codimension two, which cannot be quadratically flattened at a CR singular point but is CR non-minimal at any CR point. This provides a counter-example to a question asked in a private communication by Zaistev (2013).

Original languageEnglish (US)
Pages (from-to)995-1004
Number of pages10
JournalScience China Mathematics
Issue number6
StatePublished - Jun 1 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


  • Bishop invariants
  • CR singular points
  • Levi-flat hypersurfaces
  • holomorphic disks
  • hyperbolic structure
  • local hull of holomorphy


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