## 55 Citations

### On the isometric conjecture of Banach

- MathematicsGeometry & Topology
- 2021

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.…

### The Minkowski Measure of Asymmetry for Spherical Bodies of Constant Width

- MathematicsWuhan University Journal of Natural Sciences
- 2022

In this paper, we introduce the Minkowski measure of asymmetry for the spherical bodies of constant width. Then we prove that the spherical balls are the most symmetric bodies among all spherical…

### On Wendel’s equality for intersections of balls

- MathematicsAequationes mathematicae
- 2022

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

- Mathematics
- 2022

. 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 formulations, but rather…

### Reflections of convex bodies and their sections

- Mathematics
- 2022

. 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

- Mathematics
- 2022

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

- MathematicsJournal of Symbolic Computation
- 2022

### Projections and generated cones of homothetic convex sets

- MathematicsBeiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
- 2022