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- W2022321022 abstract "Let $Msubset mathbb{C}^2$ be a connected real-analytic hypersurface containing a connected complex hypersurface $Esubset mathbb{C}^2$ , and let $fcolon Mto mathbb{C}^2$ be a smooth CR mapping sending M into another real-analytic hypersurface $M'subset mathbb{C}^2$ . In this paper, we prove that if f does not collapse E to a point and does not collapse M into the image of E, and if the Levi form of M vanishes to first order along E, then f is real-analytic in a neighborhood of E. In general, the corresponding statement is false if the Levi form of M vanishes to second order or higher, in view of an example due to the author. We also show analogous results in higher dimensions provided that the target M' satisfies a certain nondegeneracy condition. The main ingredient in the proof, which seems to be of independent interest, is the prolongation of the system defining a CR mapping sending M into M' to a Pfaffian system on M with singularities along E. The nature of the singularity is described by the order of vanishing of the Levi form along E." @default.
- W2022321022 created "2016-06-24" @default.
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- W2022321022 date "2002-03-01" @default.
- W2022321022 modified "2023-10-15" @default.
- W2022321022 title "On the analyticity of CR mappings between nonminimal hypersurfaces" @default.
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- W2022321022 doi "https://doi.org/10.1007/s002080200007" @default.
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