arXiv subjects

Hichame Amal

Publications and source records attributed to Hichame Amal.

4 recordsLinked to original sources

arXiv2026

Maximal subextension of $m$-subharmonic functions

In this paper, we prove that given a quasi-$m$-hyperconvex domain $Ω\subset X$ in a compact Kähler manifold $(X, ω)$, and a function $φ$ in the weighted energy class $\mathcal{E}_χ^m(Ω, ω)$ with respect to a convex weight function $χ: \mathbb{R} \to \mathbb{R}$, then there exists a maximal $ω$-$m$-subharmonic subextension $\tildeφ$ to $X$ that preserves the weighted energy and satisfies a good control properties for its Hessian measure $ \mathbf{1}_ΩH_m(\tildeφ) \leq \mathbf{1}_ΩH_m(φ) $. In the last part, we study the particular case where $(X,ω)=(\mathbb{P}^n,ω_{FS}).$

math.CV↗

arXiv2025

Subextension and approximation of $m$-subharmonic functions with given boundary values

In this paper we establish a result on subextension of $m$-subharmonic functions in the class $\mathcal{F}_m(Ω,f)$ without changing the hessian measures. As application, we approximate a $m$-subharmonic function with given boudary value by an increasing sequence of $m$-subharmonic functions defined on larger domains.

math.CV↗

arXiv2025

The Hessian equation in quaternionic space

In this paper, we introduce $m$-subharmonic functions in quaternionic space $\mathbb{H}^{n}$, we define the quaternionic Hessian operator and solve the homogeneous Dirichlet problem for the quaternionic Hessian equation on the unit ball with continuous boundary data.

math.CV↗

arXiv2024

A variational approach to the quaternionic Hessian equation

In this paper, we introduce finite energy classes of quaternionic $m$-plurisubharmonic functions of Cegrell type and define the quaternionic $m$-Hessian operator on some Cegrell's classes. We use the variational approach to solve the quaternionic $m$-Hessian equation when the right-hand side is a positive Radon measure.

math.CV↗