Hartogs-Bochner type theorem in projective space

Sarkis, Frédéric

doi:10.1007/bf02384573

Cited by 6 publications

(3 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For more results and questions on particular domains (bounded or unbounded) we refer to [3,4,5,6,11,15,16,22,32]. It may also be interesting to study domains obtained by intersecting smoothly bounded domains in CP 2 with C 2 , for example with respect to extension from parts of the boundary, see [26] for domains in C 2 and further references.…”

Section: Introductionmentioning

confidence: 99%

On the Hartogs extension theorem for unbounded domains inℂn

Boggess¹,

Dwilewicz²,

Porten³

2022

Annales De l'Institut Fourier

View full text Add to dashboard Cite

Let Ω ⊂ C n , n 2, be a domain with smooth connected boundary. If Ω is relatively compact, the Hartogs-Bochner theorem ensures that every CR distribution on ∂Ω has a holomorphic extension to Ω. For unbounded domains this extension property may fail, for example if Ω contains a complex hypersurface. The main result in this paper tells that the extension property holds if and only if the envelope of holomorphy of C n \ Ω is C n . It seems that it is the first result in the literature which gives a geometric characterization of unbounded domains in C n for which the Hartogs phenomenon holds.Comparing this to earlier work by the first two authors and Z. Słodkowski, one observes that the extension problem changes in character if one restricts to CR functions of higher regularity.Résumé. -Soit Ω ⊂ C n , n 2, un domaine à bord lisse et connexe. Si Ω est relativement compact, le théorème de Hartogs et Bochner assure que toute distribution CR définie sur ∂Ω admet une extension holomorphe à Ω. Cela ne se généralise pas forcément aux domaines non-bornés, par exemple si Ω contient une hypersurface complexe. Le résultat principal de l'article dit que la propriété d'extension holomorphe a lieu si et seulement si l'enveloppe d'holomorphie de C n \Ω est C n . Il apparaît que cela est le premier résultat connu à donner une caracterisation géometrique des domaines non-bornés pour lesquels le phénomène de Hartogs est valide.En se référant à des résultats antérieurs des deux premiers auteurs et Z. Słodkowski, on constate que le problème d'extension change de nature si on se restreint à des fonctions CR plus régulières.

show abstract

Section: Introductionmentioning

confidence: 99%

On the Hartogs extension theorem for unbounded domains inℂn

Boggess¹,

Dwilewicz²,

Porten³

2022

Annales De l'Institut Fourier

View full text Add to dashboard Cite

show abstract

“…For more results and questions on particular domains (bounded or unbounded) we refer to [3,4,5,6,11,15,16,22,33]. It may also be interesting to study domains obtained by intersecting smoothly bounded domains in CP 2 with C 2 , for example with respect to extension from parts of the boundary, see [26] for domains in C 2 and further references.…”

Section: Introductionmentioning

confidence: 99%

On the Hartogs extension theorem for unbounded domains in $\mathbb{C}^n$

Boggess¹,

Dwilewicz²,

Porten³

2017

Preprint

View full text Add to dashboard Cite

show abstract

“…Historically it started with the classical theorem of Hartogs [6] in 1906. Then many versions and generalizations of this property were considered in complex analysis, algebraic geometry and partial differential equations, see, for instance, Ehrenpreis [5], Kohn and Rossi [9], Ivashkovich [8], Laurent-Thiebaut [11], Harvey and Lawson [7], Dolbeault and Henkin [2], Sarkis [12,13], Andreotti and Hill [1], Dwilewicz [3], Dwilewicz and Merker [4] and many others.…”

Section: Introductionmentioning

confidence: 99%

Holomorphic extensions in complex fiber bundles

Dwilewicz

2006

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

The main result of this paper is the existence of solutions of the equation ∂u = ω for closed (0, 1)-forms with compact support in a complex fiber bundle from some class. This class of bundles contains, for example, vector bundles. What is important, the solution exists for any base manifold. The solvability property implies many results about extension and representation of complex analytic and Cauchy-Riemann functions: Riemann-Hilbert type representation, Hartogs and Hartogs-Bochner phenomena, vanishing of some cohomology groups, to mention few.

show abstract

Hartogs-Bochner type theorem in projective space

Cited by 6 publications

References 25 publications

On the Hartogs extension theorem for unbounded domains inℂn

On the Hartogs extension theorem for unbounded domains inℂn

On the Hartogs extension theorem for unbounded domains in $\mathbb{C}^n$

Holomorphic extensions in complex fiber bundles

Contact Info

Product

Resources

About