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arXiv · 2607.19132

Maximal subextension of $m$-subharmonic functions

Hichame Amal·Ayoub El-Gasmi
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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 $(X,\omega)=(\mathbb{P}^n,\omega_{FS}).$

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Hichame Amal, Ayoub El-Gasmi. 2026-07-21. Maximal subextension of $m$-subharmonic functions. https://arxiv.org/abs/2607.19132

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