On the analyticity of CR mappings between nonminimal hypersurfaces
| dc.creator | Ebenfelt, Peter | |
| dc.date | 2000-09-01 | |
| dc.date.accessioned | 2026-07-07T04:37:06Z | |
| dc.date.available | 2026-07-07T04:37:06Z | |
| dc.description | Let M be a connected real-analytic hypersurface in two dimensional complex space, $\mathbb C^2$, containing a connected complex hypersurface E, and let f be a smooth CR mapping sending M into another real-analytic hypersurface M' in $\mathbb C^2$. 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. | |
| dc.description | 19pp; LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0009010 | |
| dc.identifier | http://arxiv.org/abs/math/0009010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59839 | |
| dc.subject | Complex Variables | |
| dc.subject | 32H40, 32V10 | |
| dc.title | On the analyticity of CR mappings between nonminimal hypersurfaces | |
| dc.type | text |