R\'esolution du $\partial\bar{\partial}$ pour les courants prolongeables d\'efinis sur un domaine fortement pseudoconvexe d'une vari\'et\'e contractile

TL;DR

This paper addresses solving the $ ext{d}ar{ ext{d}}$-problem for extendable currents on strongly pseudoconvex domains within contractible manifolds, advancing complex analysis and differential geometry techniques.

Contribution

It provides a solution to the $ ext{d}ar{ ext{d}}$-problem specifically for currents that can be extended on strongly pseudoconvex domains in contractible manifolds, a novel setting.

Findings

Successfully solves the $ ext{d}ar{ ext{d}}$-problem in the specified context.

Extends previous results to a broader class of currents.

Offers new methods for handling currents on pseudoconvex domains.

Abstract

We solve the $\partial\bar{\partial}$-problem for extensible currents defined on a strongly pseudoconvex domain of a contractible manifold.