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| HAL: hal-00003369, version 1 |
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| Global minimality of generic manifolds and holomorphic extendibility of CR functions |
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| Joel Merker 1 |
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| (1993) |
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| Let M be a smooth generic submanifold of C^n. Tumanov showed that the direction of CR extendability parallel propagates with respect to a certain differential geometric partial connection in a quotient bundle of the normal bundle to M. M is said to be globally minimal at a point z in M if the CR orbit of z contains a neighborhood of z in M. It is shown that the vector space generated by the directions of CR-extendability of CR functions on M is preserved by the induced composed flow between two points in the same CR orbit. As an application, the main result of this paper, conjectured by J.-M. Trépreau in 1990, is established: for wedge extendability of CR functions to hold at every point in the CR-orbit of z in M, it is sufficient that M be globally minimal at z. |
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| 1: | Laboratoire d'Analyse, Topologie, Probabilités (LATP) |
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CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III |
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| Subject | : | Mathematics/Differential Geometry Mathematics/Complex Variables |
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| Generic submanifolds of C^n – Global minimality in the sense of Trepreau-Tumanov – CR functions – wedges – CR-extension – propagation of holomorphic extendability |
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| hal-00003369, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00003369 | |
| oai:hal.archives-ouvertes.fr:hal-00003369 | |
| From: Joel Merker | |
| Submitted on: Saturday, 27 November 2004 14:48:10 | |
| Updated on: Sunday, 28 November 2004 09:47:37 | |
