Piercing Hyperplane Theorem

Burak Ünveren; Guy Barokas

doi:10.1134/S0001434624030349

Piercing Hyperplane Theorem

Burak Ünveren, Guy Barokas

Research output: Contribution to journal › Article › peer-review

Abstract

Abstract: We prove that any strictly convex and closed set in is an affine subspace if it contains a hyperplane as a subset. In other words, no hyperplane fits into a strictly convex and closed set unless is flat. We also present certain applications of this result in economic theory reminiscent of the separating and supporting hyperplane theorems.

Original language	English
Pages (from-to)	626-629
Number of pages	4
Journal	Mathematical Notes
Volume	115
Issue number	3-4
DOIs	https://doi.org/10.1134/S0001434624030349
State	Published - 1 Apr 2024
Externally published	Yes

Keywords

convex geometry
mathematical economics

ASJC Scopus subject areas

General Mathematics

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10.1134/S0001434624030349

Cite this

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abstract = "Abstract: We prove that any strictly convex and closed set in is an affine subspace if it contains a hyperplane as a subset. In other words, no hyperplane fits into a strictly convex and closed set unless is flat. We also present certain applications of this result in economic theory reminiscent of the separating and supporting hyperplane theorems.",

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AU - Barokas, Guy

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Y1 - 2024/4/1

N2 - Abstract: We prove that any strictly convex and closed set in is an affine subspace if it contains a hyperplane as a subset. In other words, no hyperplane fits into a strictly convex and closed set unless is flat. We also present certain applications of this result in economic theory reminiscent of the separating and supporting hyperplane theorems.

AB - Abstract: We prove that any strictly convex and closed set in is an affine subspace if it contains a hyperplane as a subset. In other words, no hyperplane fits into a strictly convex and closed set unless is flat. We also present certain applications of this result in economic theory reminiscent of the separating and supporting hyperplane theorems.

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DO - 10.1134/S0001434624030349

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Piercing Hyperplane Theorem

Abstract

Keywords

ASJC Scopus subject areas

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