Feuilletages holomorphes locaux et analyticité partielle d'applications C
∞ |
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Authors: | Sylvain Damour |
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Institution: | (1) Laboratoire d'Analyse, Topologie et Probabilités, UMR 6632, CMI, Uni- versité de Provence, 39, rue Joliot-Curie, 13453 Marseille Cedex 13, France. e-mail: Sylvain.Damour@cmi.univ-mrs.fr, FR |
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Abstract: | Let f : M → M′ be a smooth CR mapping between a generic real analytic submanifold M ⊂ ℂ
n
, n > 1, and a real analytic subset M′ ⊂ ℂ
n′
. We prove that if M is minimal and if M′ does not contain any complex curves, then f is analytic on a dense open subset of M. More generally, we establish an upper estimate of the partial analyticity of f, which depends on the maximal dimension of local holomorphic foliations contained in M
′
.
Received: 7 August 2001
Mathematics Subject Classification (2000): 32V25, 32V40, 32H99 |
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Keywords: | |
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