@inproceedings{Martini2019BodiesOC,
title={Bodies of Constant Width},
author={Horst Martini and Luis Pedro Montejano and Deborah Oliveros},
year={2019}
}

Let $V$ be a Banach space where for fixed $n$, $1<n<\dim(V)$, all of its $n$-dimensional subspaces are isometric. In 1932, Banach asked if under this hypothesis $V$ is necessarily a Hilbert space.… Expand

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We consider the width XT (ω) of a convex n-gon T in the plane along the random direction ω ∈ R/2πZ and study its deviation rate: δ(XT ) = √ E(X2 T )− E(XT )2 E(XT ) . We prove that the maximum is… Expand

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

2022

Bodies of constant width and their properties have been known for centuries. Leonard Euler, for example, studied them in the eighteenth century under the name of orbiforms. They have received… Expand