M. Dostert

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20182022

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math.MG2020

Semidefinite programming bounds for the average kissing number

Maria Dostert, Alexander Kolpakov, Fernando Mário de Oliveira Filho

The average kissing number of $R^{n}$ is the supremum of the average degrees of contact graphs of packings of finitely many balls (of any radii) in $R^{n}$ . We provid…

math.MG2019

Kissing number in spherical space

Maria Dostert, Alexander Kolpakov

This paper investigates the behaviour of the kissing number $κ (n, r)$ of congruent radius $r > 0$ spheres in $S^{n}$ , for $n \geq 2$ . Such a quantity depends on the radius $r…

math.MG2019

Kissing number in hyperbolic space

Maria Dostert, Alexander Kolpakov

This paper provides upper and lower bounds on the kissing number of congruent radius $r > 0$ spheres in $H^{n}$ , for $n \geq 2$ . For that purpose, the kissing number is repla…

math.MG2018

New dense superball packings in three dimensions

Maria Dostert, Frank Vallentin

In this paper we construct a new family of lattice packings for superballs in three dimensions (unit balls for the $l_{3}^{p}$ norm) with $p \in (1, 1.58]$ . We conjecture that the fami…