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 …

This paper deals with four symmetrizations of a convex set C: the intersection, the harmonic
and the arithmetic mean, and the convex hull of C and− C. A well-known result of Firey …

We study geometric inequalities for the circumradius and diameter with respect to general
gauges, partly also involving the inradius and the Minkowski asymmetry. There are a …

Similar to the arithmetic-harmonic mean inequality for numbers, the harmonic mean of two
convex sets K and C is always contained in their arithmetic mean. The harmonic and …

We provide a study of Blaschke–Santaló diagrams, ie complete systems of inequalities, for
the inradius, diameter, and circumradius, measured with respect to different gauges. This …

We solve several new sharp inequalities relating three quantities amongst the area,
perimeter, inradius, circumradius, diameter, and minimal width of planar convex bodies. As a …

A bounded subset of a (finite or infinite dimensional) normed linear space is said to be
complete (or diametrically complete) if it cannot be enlarged without increasing its diameter …

We study the following question: for given d⩾ 2, n⩾ d and k⩽ n, what is the largest value c
(d, n, k) such that from any set of n unit vectors in R d, we may select k vectors with …

We provide a study of Blaschke-Santal\'o diagrams for the inradius, diameter, and
circumradius, measured with respect to different gauges. This contrasts previous works on …

A gauge γ γ in a vector space X is a distance function given by the Minkowski functional
associated to a convex body K containing the origin in its interior. Thus, the outcoming …