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↗