Solving the ∂ ∂ with prescribed support

2025/11/27 by Ingoba, Winnie Ossete, Sambou, Souhaibou, Sambou, Salomon
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · doi:10.48550/arxiv.2511.22257

openalex publication_date 2025/11/27 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the problem of solving the ∂ ∂ with prescribed support for forms or currents in a domain Ω of an complex manifold X.

Citations

• Bott-Chern cohomology and the Hartogs extension theorem for pluriharmonic functions

Related

• The ∂ ∂-problem for a differential forms with boundary value in currents sense defined in a contractible completely strictly pseudoconvex domain of a complex manifold
• Résolution du ∂∂ pour les courants prolongeables définis sur un domaine fortement pseudoconvexe d'une variété contractile
• Résolution du ∂ ∂ pour les formes différentielles ayant une valeur au bord au sens des courants définies dans un domaine contractile fortement pseudoconvexe d'une variété complexe
• The ∂-equation, duality, and holomorphic forms on a reduced complex space
• Solving the ∂ ∂ for extendable currents without vanishing the boundary cohomology group