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Mathematics > Complex Variables

arXiv:1812.05811 (math)
[Submitted on 14 Dec 2018 (v1), last revised 17 Dec 2018 (this version, v2)]

Title:Meromorphically normal families and a meromorphic Montel-Carathéodory theorem

Authors:Gopal Datt
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Abstract:In this paper, we present various sufficient conditions for a family of meromorphic mappings on a domain $D\subset \mathbb{C}^m$ into $\mathbb{P}^n$ to be meromorphically normal. Meromorphic normality is a notion of sequential compactness in the meromorphic category introduced by Fujimoto. We give a general condition for meromorphic normality that is influenced by Fujimoto's work. The approach to proving this result allows us to establish meromorphic analogues of several recent results on normal families of $\mathbb{P}^n$-valued holomorphic mappings. We also establish a meromorphic version of the Montel-Carathéodory theorem.
Comments: 13 pages
Subjects: Complex Variables (math.CV)
MSC classes: 32A19, 32H04, 32Q45
Report number: Comput. Methods Funct. Theory 22, 307--321 (2022)
Cite as: arXiv:1812.05811 [math.CV]
  (or arXiv:1812.05811v2 [math.CV] for this version)
  https://doi.org/10.48550/arXiv.1812.05811
Journal reference: Computational Methods and Function Theory (2022)
Related DOI: https://doi.org/10.1007/s40315-021-00413-5

Submission history

From: Gopal Datt [view email]
[v1] Fri, 14 Dec 2018 08:04:52 UTC (16 KB)
[v2] Mon, 17 Dec 2018 13:49:13 UTC (16 KB)
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