Conjecture de Globevnik-Stout et theoreme de Morera pour une chaine holomorphe
| dc.creator | Dinh, Tien-Cuong | |
| dc.date | 1998-04-16 | |
| dc.date.accessioned | 2026-07-07T05:24:25Z | |
| dc.date.available | 2026-07-07T05:24:25Z | |
| dc.description | Let $D\subset\subset\mathbb{C}^n$ be a complex manifold of dimension $p\geq 2$ with $\C^2$ boundary in $\mathbb{C}^n$. Let $f$ be a $\C^1$ function on $bD$ and $V$ a generic and large enough family of complex $(n-p+1)$-planes. Let suppose that for $ν\in V$, no connected component of $bD\cap \mathbb{C}^{n-p+1}_ν$ is "almost" real analytic and that $f$ extends holomorphically in $D\cap\mathbb{C}^{n-p+1}_ν$. Then $f$ extend as a holomorphic function in $D$. In a special case, this result gives a partial answer to a conjecture of Globevnik-Stout. By generalizing the theorem of Harvey-Lawson, we prove a Morera type theorem for the boundary problem in $\mathbb{C}^n$ which answer to a problem asked by Dolbeault and Henkin. | |
| dc.description | 24 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/9804079 | |
| dc.identifier | http://arxiv.org/abs/math/9804079 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76832 | |
| dc.subject | Complex Variables | |
| dc.title | Conjecture de Globevnik-Stout et theoreme de Morera pour une chaine holomorphe | |
| dc.type | text |