Moduli of rotundity and smoothness for convex bodies.
Clemente Zanco, Adele Zucchi (1990)
Extracta Mathematicae
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Clemente Zanco, Adele Zucchi (1990)
Extracta Mathematicae
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Tomasz Kobos (2013)
Annales Polonici Mathematici
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The main goal of this paper is to provide an alternative proof of the following theorem of Petty: in a normed space of dimension at least three, every 3-element equilateral set can be extended to a 4-element equilateral set. Our approach is based on the result of Kramer and Németh about inscribing a simplex into a convex body. To prove the theorem of Petty, we shall also establish that for any three points in a normed plane, forming an equilateral triangle of side p, there exists a fourth...
Abdelhakim Maâden (1995)
Collectanea Mathematica
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Alexander E. Litvak, Vitali D. Milman, Nicole Tomczak-Jaegermann (2010)
Studia Mathematica
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In this note we introduce a notion of essentially-Euclidean normed spaces (and convex bodies). Roughly speaking, an n-dimensional space is λ-essentially-Euclidean (with 0 < λ < 1) if it has a [λn]-dimensional subspace which has further proportional-dimensional Euclidean subspaces of any proportion. We consider a space X₁ = (ℝⁿ,||·||₁) with the property that if a space X₂ = (ℝⁿ,||·||₂) is "not too far" from X₁ then there exists a [λn]-dimensional subspace E⊂ ℝⁿ such that E₁ = (E,||·||₁)...
Baronti, Marco, Papini, Pier Luigi (1992)
Mathematica Pannonica
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V. Klee, P. Gritzmann (1992)
Discrete & computational geometry
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V. Klee (1969)
Studia Mathematica
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Lindquist, Norman F. (1975)
Portugaliae mathematica
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Marek Cúth, Ondřej F. K. Kalenda (2015)
Colloquium Mathematicae
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We collect several variants of the proof of the third case of the Bessaga-Klee relative classification of closed convex bodies in topological vector spaces. We were motivated by the fact that we have not found anywhere in the literature a complete correct proof. In particular, we point out an error in the proof given in the book of C. Bessaga and A. Pełczyński (1975). We further provide a simplified version of T. Dobrowolski's proof of the smooth classification of smooth convex bodies...
Victor Klee, Elisabetta Maluta, Clemente Zanco (1986)
Fundamenta Mathematicae
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Daniel Azagra, Mar Jiménez-Sevilla (2002)
Extracta Mathematicae
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Abdelhakim Maaden (2002)
Extracta Mathematicae
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Dorn, C. (1978)
Portugaliae mathematica
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