2016/03/29 by Chirvasitu, Alexandru
#46C15 #47L10 #52A20 #52A21 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1603.08651
A subset of a convex body B containing the origin in a Euclidean space is \it parkable in B if it can be translated inside B in such a manner that the translate the origin. We provide characterizations of ellipsoids and of centrally symmetric convex bodies in Euclidean spaces of dimension ≥ 3 based on the notion of parkability, answering several questions posed by G. Bergman. The techniques used, which are based on characterizations of Hilbert spaces among finite-dimensional Banach spaces in terms of their lattices of subspaces and algebras of endomorphisms, also apply to improve a result of W. Blaschke characterizing ellipsoids in terms of boundaries of illumination.