manuscripta mathematica

, Volume 109, Issue 2, pp 203-222

First online:

Feuilletages holomorphes locaux et analyticité partielle d'applications C

  • Sylvain DamourAffiliated withLaboratoire 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

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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 .