The classification of holomorphic $(m,n)$--subharmonic morphisms
Complex Variables
2019-03-01 v2 Classical Analysis and ODEs
Abstract
We study the problem of classifying the holomorphic -subharmonic morphisms in complex space. This determines which holomorphic mappings preserves -subharmonicity in the sense that the composition of the holomorphic mapping with a -subharmonic functions is -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.
Cite
@article{arxiv.1806.07756,
title = {The classification of holomorphic $(m,n)$--subharmonic morphisms},
author = {Per Ahag and Rafal Czyz and Lisa Hed},
journal= {arXiv preprint arXiv:1806.07756},
year = {2019}
}