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<p>We study the boundary behaviour of a variant of the Fridman’s function (defined in terms of the Bergman metric) on Levi corank one domains, strongly pseudoconvex domains, smoothly bounded convex domains in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12044_2025_828_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> and polyhedral domains in <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12044_2025_828_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\( {\mathbb {C}}^2 \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>. Two examples are given to show that this invariant detects (local) strong pseudoconvexity of domain from its boundary behaviour.</p>

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The Bergman–Fridman invariant on some classes of pseudoconvex domains

  • 期刊论文

  • 发表日期：

    2025年6月25日

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  • Rahul Kumar,
  • Prachi Mahajan

摘要

We study the boundary behaviour of a variant of the Fridman’s function (defined in terms of the Bergman metric) on Levi corank one domains, strongly pseudoconvex domains, smoothly bounded convex domains in \( {\mathbb {C}}^n \) C n and polyhedral domains in \( {\mathbb {C}}^2 \) C 2 . Two examples are given to show that this invariant detects (local) strong pseudoconvexity of domain from its boundary behaviour.