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arXiv · 1806.07756

The classification of holomorphic $(m,n)$--subharmonic morphisms

Per Ahag·Rafal Czyz·Lisa Hed
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Abstract

We study the problem of classifying the holomorphic $(m,n)$-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 in the sense of the Caffarelli-Nirenberg-Spruck framework.

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Per Ahag, Rafal Czyz, Lisa Hed. 2018-06-20. The classification of holomorphic $(m,n)$--subharmonic morphisms. https://doi.org/10.1080/17476933.2019.1574773

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