On compact sets with a certain affine invariant

被引：0
|
作者：
A. S. Voynov
机构：
[1] Moscow State University,
来源：
Mathematical Notes | 2011年 / 90卷
关键词：
compact set; symmetry; affine symmetry; convex body; ellipsoid; John ellipsoid; Lebesgue measure; second-order hypersurface;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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