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<p>In this paper, we study the geometric properties of <i>j</i>-metric balls in certain proper non-pseudoconvex domains of <InlineEquation ID="IEq3"> <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>. We establish necessary and sufficient conditions on the centers and radii under which these balls are pseudoconvex or holomorphically convex. Our analysis covers several model domains, including the punctured space, the punctured unit ball, the complement of the unit ball, and a cone domain, and provides a framework for extending the Levi problem to <i>j</i>-metric balls in non-pseudoconvex settings.</p>

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Some properties of pseudoconvex j-metric balls of a proper domain in \({\mathbb {C}}^n\) not pseudoconvex

  • 期刊论文

  • 发表日期：

    2025年9月25日

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  • Hedi Khedhiri

摘要

In this paper, we study the geometric properties of j-metric balls in certain proper non-pseudoconvex domains of \({\mathbb {C}}^n\) C n . We establish necessary and sufficient conditions on the centers and radii under which these balls are pseudoconvex or holomorphically convex. Our analysis covers several model domains, including the punctured space, the punctured unit ball, the complement of the unit ball, and a cone domain, and provides a framework for extending the Levi problem to j-metric balls in non-pseudoconvex settings.