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Asymmetry of convex sets with isolated extreme points


Author: Gabor Toth
Journal: Proc. Amer. Math. Soc. 137 (2009), 287-295
MSC (2000): Primary 52A05; Secondary 52A38, 52B11
DOI: https://doi.org/10.1090/S0002-9939-08-09499-9
Published electronically: June 30, 2008
MathSciNet review: 2439452
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Abstract: When measuring asymmetry of convex sets $ \mathcal{L}\subset\br^n$ in terms of inscribed simplices, the interior of $ \mathcal{L}$ naturally splits into regular and singular sets. Based on examples, it may be conjectured that the singular set is empty iff $ \mathcal{L}$ is a simplex. In this paper we prove this conjecture with the additional assumption that $ \mathcal{L}$ has at least $ n$ isolated extreme points on its boundary.


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Additional Information

Gabor Toth
Affiliation: Department of Mathematics, Rutgers University, Camden, New Jersey 08102
Email: gtoth@camden.rutgers.edu

DOI: https://doi.org/10.1090/S0002-9939-08-09499-9
Received by editor(s): July 2, 2007
Received by editor(s) in revised form: January 2, 2008
Published electronically: June 30, 2008
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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