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<p>We prove that two compact subsets of complex space <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="454_2024_679_Article_IEq3.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> with corresponding complex homothetic sections (projections) are complex homothetic. The proof uses a new Helly-type theorem for cosets of closed subgroups of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="454_2024_679_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {S}^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">S</mi> </mrow> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation>.</p>

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Complex Homothetic Sections and Projections Through a Helly Type Theorem for Cosets of \(\mathbb {S}^1\)

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月13日

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  • Jorge Luis Arocha,
  • Javier Bracho,
  • Luis Montejano

摘要

We prove that two compact subsets of complex space \(\mathbb {C}^n\) C n with corresponding complex homothetic sections (projections) are complex homothetic. The proof uses a new Helly-type theorem for cosets of closed subgroups of \(\mathbb {S}^1\) S 1 .