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arXiv · 1603.08651

Parkable convex sets and finite-dimensional Hilbert spaces

Alexandru Chirvasitu
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Abstract

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 $\ge 3$ 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.

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Alexandru Chirvasitu. 2016-03-29. Parkable convex sets and finite-dimensional Hilbert spaces. https://arxiv.org/abs/1603.08651

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