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<p>This paper investigates the theory of normal families in the setting of several complex variables, focusing on the total derivatives of holomorphic functions. We extend classical results, such as Zalcman’s Lemma and the Zalcman-Pang Lemma, to the case of several complex variables, providing new normality criteria for families of holomorphic functions in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40574_2025_475_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {C}}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>. As applications, we derive two normality theorems that highlight the relevance of our extended criteria.</p>

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Normal families and total derivatives in several complex variables

  • 期刊论文

  • 发表日期：

    2025年3月11日

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  • Rahul Kumar

摘要

This paper investigates the theory of normal families in the setting of several complex variables, focusing on the total derivatives of holomorphic functions. We extend classical results, such as Zalcman’s Lemma and the Zalcman-Pang Lemma, to the case of several complex variables, providing new normality criteria for families of holomorphic functions in \({\mathbb {C}}^n\) C n . As applications, we derive two normality theorems that highlight the relevance of our extended criteria.