Horst Martini Luis Montejano Déborah Oliveros An Introduction to Convex Geometry with
Applications Page 1 Bodies of Constant Width Horst Martini Luis Montejano Déborah Oliveros An …

A convex body R in Euclidean space Ed is called reduced if the minimal width Δ (K) of each
convex body K⊂ R different from R is smaller than Δ (R). This definition yields a class of …

For a convex body C in a finite dimensional real Banach space M d denote by\triangle
(C)▵(C) its thickness, ie, its minimal width with respect to the norm. A convex body R ⊂ M^ d …

For every hemisphere K supporting a spherically convex body C of the d-dimensional
sphere Sd we consider the width of C determined by K. By the thickness∆(C) of C we mean …

Is it true that a convex body K being complete and reduced with respect to some gauge body
C is necessarily of constant width, ie does it satisfy K− K= ρ (C− C) for some ρ> 0? We prove …

We present explicit constructions of centrally symmetric 2-neighborly d-dimensional
polytopes with about 3^ d/2 ≈ (1.73)^ d vertices and of centrally symmetric k-neighborly d …

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A convex body K in ℝ d is said to be reduced if the minimum width of each convex body
properly contained in K is strictly smaller than the minimum width of K. We study the question …

A convex body $ R $ in $\mathbb R^ d $ is called reduced if the minimal width $\Delta (R') $
of each convex body $ R'\subset R $ different from $ R $ is strictly smaller than the minimal …

Let d≥ 2, m≥ d, and u1,..., um be non-zero vectors linearly spanning Rd. We consider the
class P (u1,..., um) of convex polytopes P in Rd such that P= conv (I1∪...∪ Im), where, for j …