, Volume 109, Issue 2, pp 203-222

Feuilletages holomorphes locaux et analyticité partielle d'applications C

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 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