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On envelopes of holomorphy of domains covered by Levi-flat hats and the reflection principle. (English) Zbl 1031.32028

Let \(h: M\rightarrow M'\) be a \(C^\infty\)-smooth CR diffeomorphism between two smooth real analytic hypersurfaces in \(\mathbb C^n\) with \(n\geq 2\). \(M\) is called globally minimal if it consists of a single CR orbit. \(M'\) is called holomorphically nondegenerate if there does not exist any nonzero \((1,0)\) tangent vector field with holomorphic coefficients.
The main result in this paper is as follows. If \(M\) is globally minimal and if \(M'\) is holomorphically nondegenerate, then any \(C^\infty\)-smooth diffeomorphism \(h\) is real analytic at every point of \(M\).

MSC:

32V25 Extension of functions and other analytic objects from CR manifolds
32V40 Real submanifolds in complex manifolds
32V10 CR functions
32D10 Envelopes of holomorphy
32D20 Removable singularities in several complex variables
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