Maximal subextension of m-subharmonic functions

2026/07/21 by Hichame Amal, Ayoub El-Gasmi
Mathematics · #math.CV

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Abstract

In this paper, we prove that given a quasi-m-hyperconvex domain Ω⊂ X in a compact Kähler manifold (X, ω), and a function φ in the weighted energy class E_χ^m(Ω, ω) with respect to a convex weight function χ: ℝ → ℝ, then there exists a maximal ω-m-subharmonic subextension φ to X that preserves the weighted energy and satisfies a good control properties for its Hessian measure 1_ΩH_m(φ) ≤ 1_ΩH_m(φ) . In the last part, we study the particular case where (X,ω)=(ℙⁿ,ω_FS).

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