Complex homothetic sections and projections through a Helly type Theorem for cosets of \(\S^1\)

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

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Bibliographic Details
Published inarXiv.org
Main Authors Arocha, Jorge Luis, Bracho, Javier, Montejano, Luis
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 09.10.2023
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Summary:We prove that two closed subsets of complex space \(\C^n\) with corresponding complex homothetic sections (projections) are complex homothetic. The proof uses a new Helly-type theorem for cosets of closed subgroups of \(\S ^1\).
ISSN:2331-8422