25 citations · 32 across the 7 of their papers we have counts for
4 papers · 1 filter
Centroids of sections of convex bodies and Lusternik-Schnirelmann category
Julian Haddad, C. Hugo Jiménez, Rafael Villa
Given two symmetric convex bodies with strictly convex, we prove that there exist at least hyperplanes tangent to , such that the cent…
Rogers-Shephard and local Loomis-Whitney type inequalities
David Alonso-Gutiérrez, Shiri Artstein-Avidan, Bernardo González Merino +2
We provide functional analogues of the classical geometric inequality of Rogers and Shephard on products of volumes of sections and projections. As a consequence we recover (and ob…
Maximal equilateral sets
Konrad J. Swanepoel, Rafael Villa
A subset of a normed space is called equilateral if the distance between any two points is the same. Let be the smallest possible size of an equilateral subset of ma…
A lower bound for the equilateral number of normed spaces
Konrad J Swanepoel, Rafael Villa
We show that if the Banach-Mazur distance between an n-dimensional normed space X and ell infinity is at most 3/2, then there exist n+1 equidistant points in X. By a well-known res…