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Maximal subextension of m-subharmonic functions
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 ℰχm(Ω, ω) with respect to a convex weight function χ: ℝ → ℝ, then there exists a maximal ω-m-subharmonic subextension φ̃ to X that preserves the weighted energy and satisfies good control properties for its Hessian measure 1ΩHm(φ̃) ≤ 1ΩHm(φ).
Related
- Minimal m-subharmonic functions with nonmaximal Hessian measures
- Complete harmonic metrics and subharmonic functions on the complex plane
- Endpoint power weight inequalities for spherical maximal functions
- Sharp derivative inequalities for maximal functions
- Bilinear maximal functions associated with some degenerate surfaces on the Heisenberg group
BibTeX
@misc{amal2026maximal,
title = {{Maximal subextension of $m$-subharmonic functions}},
author = {Hichame Amal and Ayoub El-Gasmi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.19132},
eprint = {2607.19132},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.19132},
}
RIS
TY - UNPB
TI - Maximal subextension of m-subharmonic functions
AU - Hichame Amal
AU - Ayoub El-Gasmi
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2607.19132
UR - https://arxiv.org/abs/2607.19132
AB - 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 φ̃ to X that preserves the weighted energy and satisfies good control properties for its Hessian measure 1_ΩH_m(φ̃) ≤ 1_ΩH_m(φ).
ER -