Bodies of Constant Width

  title={Bodies of Constant Width},
  author={Horst Martini and Luis Pedro Montejano and Deborah Oliveros},

On the isometric conjecture of Banach

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.

On Wendel’s equality for intersections of balls

We study the analogue of Wendel’s equality in random polytope models in which the hull of the random points is formed by intersections of congruent balls, called the spindle (or hyper-) convex hull.

Some extremal problems for polygons in the Euclidean plane

. The paper is devoted to some extremal problems, related to convex polygons in the Euclidean plane and their perimeters. We present a number of results that have simple statements and rather

Reflections of convex bodies and their sections

. The purpose of this paper is to study the reflections of a convex body. In particular, we are interested in orthogonal reflections of its sections that can be extended to reflections of the whole

A new duality on closed convex sets

In this paper we study a subclass of convex sets which are called closed pseudo-cones and introduce a new duality on this subclass. It turns out that the new duality characterizes closed pseudo-cones

Algebraic equations for constant width curves and Zindler curves

Projections and generated cones of homothetic convex sets

  • V. Soltan
  • Mathematics
    Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
  • 2022

Width deviation of convex polygons

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

Peabodies of constant width

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