4 papers
A short solution of the kissing number problem in dimension three
Alexey Glazyrin
In this note, we give a short solution of the kissing number problem in dimension three.
Energy on spheres and discreteness of minimizing measures
Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke +2
In the present paper we study the minimization of energy integrals on the sphere with a focus on an interesting clustering phenomenon: for certain types of potentials, optimal meas…
Moments of isotropic measures and optimal projective codes
Alexey Glazyrin
In this paper, we use the linear programming approach to find new upper bounds for the moments of isotropic measures. These bounds are then utilized for finding lower packing bound…
Stability of the simplex bound for packings by equal spherical caps determined by simplicial regular polytopes
Károly Böröczky, Károly J. Böröczky, Alexey Glazyrin +1
It is well known that the vertices of any Euclidean simplicial regular polytope determine an optimal packing of equal spherical balls. We prove a stability version of optimal order…