CR foliations, the strip-problem and Globevnik-Stout conjecture

Mark Agranovsky

doi:10.1016/j.crma.2006.06.013

CR foliations, the strip-problem and Globevnik-Stout conjecture

Mark Agranovsky

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We characterize CR functions on planar domains and real hypersurfaces in C² in terms of analytic extendibility into attached analytic discs. It is done by studying propagation, from the boundary into interior, of degeneracy of CR foliations of solid torus-like manifolds. In particular, we answer, for smooth functions, two open questions mentioned in the title: about characterization of analytic functions in the complex plane and about characterization of boundary values of holomorphic functions in bounded domains in Cⁿ. To cite this article: M. Agranovsky, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

Original language	English
Pages (from-to)	91-94
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	343
Issue number	2
DOIs	https://doi.org/10.1016/j.crma.2006.06.013
State	Published - 15 Jul 2006

Bibliographical note

Funding Information:
1 This work was partially supported by Israel Scientific Foundation, grant No. 279/02-01.

Funding

1 This work was partially supported by Israel Scientific Foundation, grant No. 279/02-01.

Funders	Funder number
Israel Scientific Foundation	279/02-01

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10.1016/j.crma.2006.06.013

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abstract = "We characterize CR functions on planar domains and real hypersurfaces in C2 in terms of analytic extendibility into attached analytic discs. It is done by studying propagation, from the boundary into interior, of degeneracy of CR foliations of solid torus-like manifolds. In particular, we answer, for smooth functions, two open questions mentioned in the title: about characterization of analytic functions in the complex plane and about characterization of boundary values of holomorphic functions in bounded domains in Cn. To cite this article: M. Agranovsky, C. R. Acad. Sci. Paris, Ser. I 343 (2006).",

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CR foliations, the strip-problem and Globevnik-Stout conjecture

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