Let M be a real hypersurface of Cn, M+ a closed half space with boundary M, zo a point of M. We prove that the existence of a disc A tangent to M at zo, attached to M+ but not to M (i.e.∂A ⊂ M+ but ∂A ⊂ M), entails extension of holomorphic functions from the interior of M+ to a full neighborhood of zo. This result covers a result in [9], where the disc A is assumed to lie on one side M+ of M. T he basic idea, which underlies to the whole paper, is due to A. Tumanov [8] and consists in attaching discs to manifolds with boundary. Further, holomorphic extendability by the aid of tangent discs attached to M and of “defect 0” is a particular case of a general theorem of “wedge extendibility” of CR–functions by A. Tumanov.
Analytic discs attached to half spaces of C^n and extension of holomorphic functions
BARACCO, LUCA;ZAMPIERI, GIUSEPPE
2001
Abstract
Let M be a real hypersurface of Cn, M+ a closed half space with boundary M, zo a point of M. We prove that the existence of a disc A tangent to M at zo, attached to M+ but not to M (i.e.∂A ⊂ M+ but ∂A ⊂ M), entails extension of holomorphic functions from the interior of M+ to a full neighborhood of zo. This result covers a result in [9], where the disc A is assumed to lie on one side M+ of M. T he basic idea, which underlies to the whole paper, is due to A. Tumanov [8] and consists in attaching discs to manifolds with boundary. Further, holomorphic extendability by the aid of tangent discs attached to M and of “defect 0” is a particular case of a general theorem of “wedge extendibility” of CR–functions by A. Tumanov.
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