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<p>In this paper, we have shown that any univalent map from a strongly convex domain <i>D</i> in <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> onto a bounded strongly pseudoconvex domain <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\Omega \subset \mathbb {C}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Ω</mi> <mo>⊂</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>n</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> with certain boundary regularity can be embedded into a certain Loewner chain if and only if <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\overline{\Omega }\)</EquationSource> <EquationSource Format="MATHML"><math> <mover> <mi mathvariant="normal">Ω</mi> <mo>¯</mo> </mover> </math></EquationSource> </InlineEquation> is polynomially convex.</p>

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Embedding of an univalent map on a bounded strongly convex domain in \(\mathbb {C}^{n}\) into a Loewner chain

  • 期刊论文

  • 发表日期：

    2025年12月20日

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  • Sanjoy Chatterjee,
  • Sushil Gorai

摘要

In this paper, we have shown that any univalent map from a strongly convex domain D in \(\mathbb {C}^n\) C n onto a bounded strongly pseudoconvex domain \(\Omega \subset \mathbb {C}^n\) Ω ⊂ C n with certain boundary regularity can be embedded into a certain Loewner chain if and only if \(\overline{\Omega }\) Ω ¯ is polynomially convex.