New volume ratio properties for convex sym-metric bodies in IRn.
J. Bourgain, V.D. Milman (1987)
Inventiones mathematicae
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J. Bourgain, V.D. Milman (1987)
Inventiones mathematicae
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Lassak, Marek (2008)
Beiträge zur Algebra und Geometrie
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Richard McGehee (1974)
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Wu-yi Hsiang, Wu-Teh Hsiang (1989)
Inventiones mathematicae
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Lassak, Marek, Nowicka, Monika (2009)
Beiträge zur Algebra und Geometrie
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Marek Lassak, Monika Nowicka (2010)
Colloquium Mathematicae
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Denote by Kₘ the mirror image of a planar convex body K in a straight line m. It is easy to show that K*ₘ = conv(K ∪ Kₘ) is the smallest by inclusion convex body whose axis of symmetry is m and which contains K. The ratio axs(K) of the area of K to the minimum area of K*ₘ over all straight lines m is a measure of axial symmetry of K. We prove that axs(K) > 1/2√2 for every centrally symmetric convex body and that this estimate cannot be improved in general. We also give a formula for...
Robert L. Devaney (1980)
Inventiones mathematicae
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Dorn, C. (1978)
Portugaliae mathematica
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Paul Goodey (2009)
Banach Center Publications
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We survey results concerning the extent to which information about a convex body's projections or sections determine that body. We will see that, if the body is known to be centrally symmetric, then it is determined by the size of its projections. However, without the symmetry condition, knowledge of the average shape of projections or sections often determines the body. Rather surprisingly, the dimension of the projections or sections plays a key role and exceptional cases do occur...
Zhang, Gaoyong (1999)
Annals of Mathematics. Second Series
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S. Smale (1970)
Inventiones mathematicae
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Gardner, R.J., Koldobsky, A., Schlumprecht, T. (1999)
Annals of Mathematics. Second Series
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V. Milman (1992)
Geometric and functional analysis
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