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Complex Homothetic Sections and Projections Through a Helly Type Theorem for Cosets of S1.

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Title: Complex Homothetic Sections and Projections Through a Helly Type Theorem for Cosets of S1.
Authors: Arocha, Jorge Luis1 (AUTHOR) jorge.l.arocha@gmail.com, Bracho, Javier1 (AUTHOR) jbracho@im.unam.mx, Montejano, Luis1 (AUTHOR) luis@im.unam.mx
Source: Discrete & Computational Geometry. Oct2025, Vol. 74 Issue 3, p805-813. 9p.
Subjects: Complex geometry, Mathematics theorems, Mathematical transformations, Mathematics, Compact spaces (Topology), Topological groups
Abstract: We prove that two compact 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 . [ABSTRACT FROM AUTHOR]
Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: We prove that two compact 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 . [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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              Text: Oct2025
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