# The $\partial \bar{\partial}$-problem for a differential forms with boundary value in currents sense defined in a contractible completely strictly pseudoconvex domain of a complex manifold

## TL;DR

This paper addresses the $ar{ar{ ext{d}}}$-problem for smooth differential forms with boundary values in currents sense, within a contractible, strictly pseudoconvex domain of a complex manifold, advancing complex analysis techniques.

## Contribution

It provides a solution to the $ar{ar{ ext{d}}}$-problem for forms with boundary values in currents sense on specific pseudoconvex domains, extending existing theory.

## Key findings

- Solved the $ar{ar{ ext{d}}}$-problem for smooth forms with boundary in currents sense.
- Established existence results in a contractible strictly pseudoconvex domain.
- Extended the theory of boundary value problems in complex analysis.

## Abstract

We solve the $\partial \bar{\partial}$-problem for the differential forms of class $C^\infty$ with boundary value in currents sense defined on a contractible completely strictly pseudoconvex domain of a complex manifold.