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Souhaibou Sambou

Publications and source records attributed to Souhaibou Sambou.

9 recordsLinked to original sources
arXiv2026

Complex Monge-Amp{è}re equations with boundary values: a variational approach

Let $Ω$ ___ C n be a bounded hyperconvex domain and $Φ$\,: $Ω$ $\rightarrow$ R a maximal plurisubharmonic function in $Ω$ (possibly unbounded). We introduce a new class E 1 $Φ$ ($Ω$) of plurisubharmonic functions with boundary values equal to $Φ$ in the sense of Cegrell and finite $Φ$-energy on $Ω$. Then given a Borel measure $μ$ on $Ω$, we apply a variational approach to prove that $μ$ is the Monge-Amp{è}re measure of a function u $\in$ E 1 $Φ$ ($Ω$) if and only if it satisfies the integrability condition We also establish a quantitative version of this condition extending previous results of Cegrell and others. Using a logarithmic transformation, we obtain analogous results for the real Monge-Amp{è}re equations with (unbounded) boundary data.

math.AP↗
arXiv2026

Introduction au $\partial\bar{\partial}$-Neumann

In this paper, we shall use the $L^2$ existence theorems for $\partial\bar{\partial}$ provide by Guy Laville to etablish for existence theorem for the $\partial\bar{\partial}$-Neumann operator on any bounded pseudoconvex starred domaine $Ω$ in $\mathbb{C}^n$ based on the work of D. Spencer on the $\bar{\partial}$-Neumann. As a result, we obtain a new method for resolving the $\partial\bar{\partial}. $

math.DG↗
arXiv2025

Generalized study of the operator $α\partial^k \bar{\partial}^{k} + β\bar{\partial}^k +γ\partial^k + c$ in weighted Hilbert space $L^2(\mathbb{C}, \mathrm{e}^{-|z|^2})$

By Hörmander's $L^2$-method, we study the operator $α\partial^k \bar{\partial}^{k} + β\bar{\partial}^k +γ\partial^k + c$ for any order $k$ with $α, β, γ\in \mathbb{R}$ such that $(α, β, γ) \neq(0,0,0)$ in the weighted Hilbert space $L^2(\mathbb{C}, \mathrm{e}^{-|z|^2})$. We prove the existence of its right inverse which is also a bounded operator. Subsequently we will study two cases that arise from this operator, namely: (1) Case where $α= γ=0$: The operator $β\bar{\partial}^{k} + c$ with $\vert β\vert \geq 1$. (2) Case where $β= γ=0$: The operator $α\partial^{k} \bar{\partial}^{k} + c$ with $\vert α\vert \geq 1$.

math.CV↗
arXiv2025

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

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 $Ω$ of a complex analytic manifold $X$. 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.

math.CV↗