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

2018/06/30 by Per Åhag, Per Ahag, Rafał Czyż +2 · 2 citations
Mathematics · #Composition (language) #Constant (computer programming) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #Holomorphic function #Holomorphic functional calculus #Identity theorem #Morphism #math.CA #math.CV #msc:15A18 #msc:31C45 #msc:32A10 #msc:32U05 #msc:58E20

paper · pdf · doi:10.1080/17476933.2019.1574773

published in Complex Variables and Elliptic Equations 65(2), 152-177 (Taylor & Francis)

arxiv created 2018/08/27 · openalex publication_date 2019/02/27 · arxiv updated 2019/03/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05

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.

Citations

• Classroom Note:A Simple Proof of the Leverrier--Faddeev Characteristic Polynomial Algorithm
• The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian
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• Calibrated geometries