Geodesic
On Compact Sets with a Certain Affine Invariant
Matematičeskie zametki, Tome 90 (2011) no. 1, pp. 34-39

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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
Mots-clés : Lebesgue measure, second-order hypersurface. 
@article{MZM_2011_90_1_a3,
     author = {A. S. Voynov},
     title = {On {Compact} {Sets} with a {Certain} {Affine} {Invariant}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {34--39},
     publisher = {mathdoc},
     volume = {90},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_1_a3/}
}
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A. S. Voynov. On Compact Sets with a Certain Affine Invariant. Matematičeskie zametki, Tome 90 (2011) no. 1, pp. 34-39. http://geodesic.mathdoc.fr/item/MZM_2011_90_1_a3/