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Matematicheskie Zametki, 2011, Volume 90, Issue 1, Pages 34–39
DOI: https://doi.org/10.4213/mzm8618 (Mi mzm8618) 		 
On Compact Sets with a Certain Affine Invariant

A. S. Voynov

M. V. Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm8618
Abstract: We give a complete characterization of finite-dimensional compact sets with the following property: all of their images under affine operators are symmetric (that is, have symmetry planes of certain dimensions). We also study the noncompact case; namely, we reveal a class of unbounded closed sets with this property and conjecture that this class is complete.
Keywords: compact set, symmetry, affine symmetry, convex body, ellipsoid, John ellipsoid, Lebesgue measure, second-order hypersurface.
Received: 09.11.2009
English version:
Mathematical Notes, 2011, Volume 90, Issue 1, Pages 32–36
DOI: https://doi.org/10.1134/S0001434611070042
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: A. S. Voynov, “On Compact Sets with a Certain Affine Invariant”, Mat. Zametki, 90:1 (2011), 34–39; Math. Notes, 90:1 (2011), 32–36
Citation in format AMSBIB
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