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On Compact Sets with a Certain Affine Invariant
A. S. Voynov M. V. Lomonosov Moscow State University
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
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
Linking options:
https://www.mathnet.ru/eng/mzm8618https://doi.org/10.4213/mzm8618 https://www.mathnet.ru/eng/mzm/v90/i1/p34
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