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Minimal m-subharmonic functions with nonmaximal Hessian measures
Abstract
For every 2≤ m≤ n, we construct Hölder continuous functions on the closed unit ball that are minimal in the Cegrell class Fm, although their Hessian measures are not maximal in the m-subharmonic ordering. This answers a question posed by the second author. We also obtain a minimality criterion based on partial pluricomplex energy and an explicit family of Monge--Ampère examples on a product domain. For m=1, minimality and maximality are equivalent on a ball.
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BibTeX
@misc{do2026minimal,
title = {{Minimal m-subharmonic functions with nonmaximal Hessian measures}},
author = {Thai Duong Do and Van Thien Nguyen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30926},
eprint = {2609.30926},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30926},
}
RIS
TY - UNPB
TI - Minimal m-subharmonic functions with nonmaximal Hessian measures
AU - Thai Duong Do
AU - Van Thien Nguyen
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.30926
UR - https://arxiv.org/abs/2609.30926
AB - For every 2≤ m≤ n, we construct Hölder continuous functions on the closed unit ball that are minimal in the Cegrell class F_m, although their Hessian measures are not maximal in the m-subharmonic ordering. This answers a question posed by the second author. We also obtain a minimality criterion based on partial pluricomplex energy and an explicit family of Monge--Ampère examples on a product domain. For m=1, minimality and maximality are equivalent on a ball.
ER -