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arXiv · 2511.22969

Solving the $\partial \overline{\partial}$ for extendable currents without vanishing the boundary cohomology group

Mamadou Eramane Bodian·Souhaibou Sambou·Sény Diatta·Salomon Sambou
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Abstract

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 $\Omega$ 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.

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Mamadou Eramane Bodian, Souhaibou Sambou, Sény Diatta, Salomon Sambou. 2025-11-28. Solving the $\partial \overline{\partial}$ for extendable currents without vanishing the boundary cohomology group. https://arxiv.org/abs/2511.22969

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