manuscripta mathematica

, Volume 109, Issue 2, pp 203–222

Feuilletages holomorphes locaux et analyticité partielle d'applications C

Authors

  • Sylvain Damour
    • 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

DOI: 10.1007/s00229-002-0300-1

Cite this article as:
Damour, S. Manuscripta Math. (2002) 109: 203. doi:10.1007/s00229-002-0300-1
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Abstract.

 Let f : M → M′ be a smooth CR mapping between a generic real analytic submanifold M ⊂ ℂn, n > 1, and a real analytic subset M′ ⊂ ℂn′. 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.

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© Springer-Verlag Berlin Heidelberg 2002