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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/2466831
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact