5 papers
How close are cone singularities on a random flat surface?
Alexey Rukhovich
We study the shortest geodesics on flat cone spheres, i.e. flat metrics on the sphere with conical singularities. The length of the shortest geodesic between two singular points ca…
Asymptotics of the number of waves on rational polyhedra
Vsevolod L. Chernyshev, Alexey Rukhovich
The problem of counting the number of waves arriving at the vertex of a polyhedron is motivated by physics. In the article it was solved for the case of Platonic solid using three…
Clique complexes of multigraphs, edge inflations, and tournaplexes
Anton Ayzenberg, Alexey Rukhovich
In this paper we introduce and study the topology of clique complexes of multigraphs without loops. These clique complexes generalize tournaplexes, which were recently introduced b…
On intersection of two embedded spheres in 3-space
Alexey Rukhovich
This article is covered by the article arxiv.1012.0925 We study intersection of two polyhedral spheres without self-intersections in 3-space. We find necessary and sufficient condi…
On intersection of two embedded spheres in 3-space
Alexey Rukhovich
We study intersection of two polyhedral spheres without self-intersections in 3-space. We find necessary and sufficient conditions on sequences x = x_1,x_2,...,x_n, y = y_1,y_2,...…