Semi-Bloch functions in several complex variables

2013/12/20 by Ulf Backlund, Ulf Bäcklund, Linus Carlsson +6
Mathematics · #30D45 #32A18 #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV #msc:30D45 #msc:32A18

paper · pdf · doi:10.48550/arxiv.1312.6053

arxiv created 2013/12/20 · openalex publication_date 2013/12/20 · arxiv updated 2013/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be an n-dimensional complex manifold. A holomorphic function f:M→ \mathbb C is said to be semi-Bloch if for every λ∈ \mathbb C the function g_λ=exp(λf(z)) is normal on M. We characterise Semi-Bloch functions on infinitesimally Kobayashi non-degenerate M in geometric as well as analytic terms. Moreover, we show that on such manifolds, semi-Bloch functions are normal.

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