On Antipodal and Adjoint Pairs of Points for Two Convex Bodies.
V. Soltan (1995)
Discrete & computational geometry
Similarity:
V. Soltan (1995)
Discrete & computational geometry
Similarity:
Alexander E. Litvak, Vitali D. Milman, Nicole Tomczak-Jaegermann (2010)
Studia Mathematica
Similarity:
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)...
U. Betke, M. Henk (1993)
Discrete & computational geometry
Similarity:
Boltyanski, V., Martini, H. (1999)
Beiträge zur Algebra und Geometrie
Similarity:
Milman, Vitali (1998)
Documenta Mathematica
Similarity:
Chuanming Zong (1994)
Discrete & computational geometry
Similarity:
L. Lovász, R. Kannan, M. Simonovits (1995)
Discrete & computational geometry
Similarity:
Tomasz Kobos (2013)
Annales Polonici Mathematici
Similarity:
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...
David G. Larman (2009)
Banach Center Publications
Similarity:
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.
J. Friedman, N. Linial (1993)
Discrete & computational geometry
Similarity:
Hausel, T., Makai, E., Szücs, A. (1997)
General Mathematics
Similarity:
P. Mani-Levitska, H.E. Debrunner (1986)
Discrete & computational geometry
Similarity:
Weißbach, Benulf (1996)
Beiträge zur Algebra und Geometrie
Similarity:
Mariano Rodríguez-Arias Fernández (1992)
Extracta Mathematicae
Similarity:
Makeev, V.V. (2005)
Journal of Mathematical Sciences (New York)
Similarity: