The classification of holomorphic (<i>m</i>, <i>n</i>)-subharmonic morphisms

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.

Locations

• arXiv (Cornell University) - View - PDF
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• Complex Variables and Elliptic Equations - View