CR-submanifold formal-equivalence conjecture of Baouendi, Rothschild, and Zaitsev

About 23 years old · traced to

Let M⊂CNM\subset\mathbb C^N be a real analytic CR submanifold. Let p∈Mp\in M, let M′⊂CNM'\subset\mathbb C^N be a real analytic submanifold with dim⁡RM=dim⁡RM′\dim_{\mathbb R}M=\dim_{\mathbb R}M', and let p′∈M′p'\in M'. Let F:(CN,p)→(CN,p′)F:(\mathbb C^N,p)\to(\mathbb C^N,p') be a formal invertible mapping sending MM into M′M'. Baouendi–Rothschild–Zaitsev CR-submanifold conjecture. The mapping FF can be approximated by holomorphic mappings as in the conclusion of the approximation theorem. This would reduce the exceptional locus to the points where the source is not CR, addressing formal equivalence versus local biholomorphic equivalence.

References

Primary source

Linda Preiss Rothschild, “Mappings between real submanifolds in complex space”, arXiv:math/0304015 (2003).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.