R{\'e}solution du $\partial \bar{\partial}$ pour les formes diff{\'e}rentielles ayant une valeur au bord au sens des courants d{\'e}finies dans un domaine contractile fortement pseudoconvexe d'une vari{\'e}t{\'e} complexe

TL;DR

This paper addresses the solution of the $ar{ar{ ext{d}}}$-problem for differential forms with boundary distributions in strongly pseudoconvex, contractible domains within complex manifolds, advancing complex analysis techniques.

Contribution

It provides a method to solve the $ar{ar{ ext{d}}}$-problem for forms with boundary values in complex manifolds, extending existing theories to new boundary conditions.

Findings

Successfully solves the $ar{ar{ ext{d}}}$-problem under specified conditions

Establishes existence of solutions for forms with distribution boundary values

Extends classical results to strongly pseudoconvex, contractible domains

Abstract

We solve the $\partial \bar{\partial}$-problem for a form with distribution boundary value on a strongly pseudoconvex contractible domain of a complex manifold.