Maximal subextension of $m$-subharmonic functions

Hichame Amal; Saïd Asserda; Ayoub El-Gasmi

Maximal subextension of $m$-subharmonic functions

Complex Variables 2026-07-21 v1

Authors: Hichame Amal , Saïd Asserda , Ayoub El-Gasmi

Abstract

In this paper, we prove that given a quasi- $m$ -hyperconvex domain $\Omega \subset X$ in a compact K\"ahler manifold $(X, \omega)$ , and a function $\varphi$ in the weighted energy class $\mathcal{E}_\chi^m(\Omega, \omega)$ with respect to a convex weight function $\chi : \mathbb{R} \to \mathbb{R}$ , then there exists a maximal $\omega$ - $m$ -subharmonic subextension $\tilde{\varphi}$ to $X$ that preserves the weighted energy and satisfies a good control properties for its Hessian measure $\mathbf{1}_\Omega H_m(\tilde{\varphi}) \leq \mathbf{1}_\Omega H_m(\varphi)$ . In the last part, we study the particular case where $(X,\omega)=(\mathbb{P}^n,\omega_{FS}).$

Cite

@article{arxiv.2607.19132,
  title  = {Maximal subextension of $m$-subharmonic functions},
  author = {Hichame Amal and Saïd Asserda and Ayoub El-Gasmi},
  journal= {arXiv preprint arXiv:2607.19132},
  year   = {2026}
}