ABSTRACT
We study the problem of classifying the holomorphic -subharmonic morphisms in complex space. This determines which holomorphic mappings preserves m-subharmonicity in the sense that the composition of the holomorphic mapping with a m-subharmonic functions is n-subharmonic. We show that there are three different scenarios depending on the underlying dimensions, and the model itself. Either the holomorphic mappings are just the constant functions, or up to composition with a homotethetic map, canonical orthogonal projections. Finally, there is a more intriguing case when subharmonicity is gained.
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Disclosure statement
No potential conflict of interest was reported by the authors.