One functional-analytical idea by Alexandrov in convex geometry.
Kutateladze, S.S. (2002)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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Kutateladze, S.S. (2002)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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Rogers, C.A. (1965)
Portugaliae mathematica
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Lindquist, Norman F. (1975)
Portugaliae mathematica
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Lindquist, Norman F. (1975)
Portugaliae mathematica
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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...
Rolf Schneider (1972)
Annales Polonici Mathematici
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Dorn, C. (1978)
Portugaliae mathematica
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David G. Larman (2009)
Banach Center Publications
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The connectivity and measure theoretic properties of the skeleta of convex bodies in Euclidean space are discussed, together with some long standing problems and recent results.
Mustafaev, Zokhrab (2004)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Mustafaev, Zokhrab (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Glasauer, Stefan (1999)
Beiträge zur Algebra und Geometrie
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Martini, Horst, Mustafaev, Zokhrab (2010)
Journal of Inequalities and Applications [electronic only]
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Makeev, V.V. (2005)
Journal of Mathematical Sciences (New York)
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