English

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

Complex Variables 2025-12-01 v1

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 Ω\Omega of a complex analytic manifold XX. 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.

Keywords

Cite

@article{arxiv.2511.22969,
  title  = {Solving the $\partial \overline{\partial}$ for extendable currents without vanishing the boundary cohomology group},
  author = {Mamadou Eramane Bodian and Souhaibou Sambou and Sény Diatta and Salomon Sambou},
  journal= {arXiv preprint arXiv:2511.22969},
  year   = {2025}
}
R2 v1 2026-07-01T07:58:57.055Z