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5 papers · 2 filters
Dehn invariant of flexible polyhedra
Alexander A. Gaifullin, Leonid Ignashchenko
We prove that the Dehn invariant of any flexible polyhedron in Euclidean space of dimension greater than or equal to 3 is constant during the flexion. In dimensions 3 and 4 this im…
Proof of László Fejes Tóth's zone conjecture
Zilin Jiang, Alexandr Polyanskii
A zone of width on the unit sphere is the set of points within spherical distance of a given great circle. We show that the total width of any collection of zones coverin…
The problem of camouflaging via mirror reflections
Alexander Plakhov
This work is related to billiards and their applications in geometric optics. It is known that perfectly invisible bodies with mirror surface do not exist. It is natural to search…
Waist of balls in hyperbolic and spherical spaces
Arseniy Akopyan, Roman Karasev
In this paper we find a tight estimate for Gromov's waist of the balls in spaces of constant curvature, deduce the estimates for the balls in Riemannian manifolds with upper bounds…
Hunting for reduced polytopes
Bernardo González Merino, Thomas Jahn, Alexandr Polyanskii +1
We show that there exist reduced polytopes in three-dimensional Euclidean space. This partially answers the question posed by Lassak on the existence of reduced polytopes in -di…