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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.22969 |
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| _version_ | 1866914173723607040 |
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| author | Bodian, Mamadou Eramane Sambou, Souhaibou Diatta, Sény Sambou, Salomon |
| author_facet | Bodian, Mamadou Eramane Sambou, Souhaibou Diatta, Sény Sambou, Salomon |
| contents | In this paper, we consider the problem of solving the $\partial\overline{\partial}$ equation with discribed support for differential forms in a relatively compact domain $Ω$ of a complex analytic manifold $X$. And as a consequence, we have the solution of the equation $\partial\overline{\partial}$ for extendable currents without the annulation assumption of the De Rham cohomology group of the boundary.\\ \textbf{Keywords:} operator $\partial\overline{\partial}$, De Rham cohomology group, Dolbeault cohomology group, Bott-Chern cohomology group,Applie cohomology group, discribed support, extendable currents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22969 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solving the $\partial \overline{\partial}$ for extendable currents without vanishing the boundary cohomology group Bodian, Mamadou Eramane Sambou, Souhaibou Diatta, Sény Sambou, Salomon Complex Variables In this paper, we consider the problem of solving the $\partial\overline{\partial}$ equation with discribed support for differential forms in a relatively compact domain $Ω$ of a complex analytic manifold $X$. And as a consequence, we have the solution of the equation $\partial\overline{\partial}$ for extendable currents without the annulation assumption of the De Rham cohomology group of the boundary.\\ \textbf{Keywords:} operator $\partial\overline{\partial}$, De Rham cohomology group, Dolbeault cohomology group, Bott-Chern cohomology group,Applie cohomology group, discribed support, extendable currents. |
| title | Solving the $\partial \overline{\partial}$ for extendable currents without vanishing the boundary cohomology group |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2511.22969 |