Kissing number in hyperbolic space
| Autor: | Dostert, Maria, Kolpakov, Alexander |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | This paper provides upper and lower bounds on the kissing number of congruent radius $r > 0$ spheres in $\mathbb{H}^n$, for $n\geq 2$. For that purpose, the kissing number is replaced by the kissing function $\kappa(n, r)$ which depends on the radius $r$. After we obtain some theoretical lower and upper bounds for $\kappa(n, r)$, we study their asymptotic behaviour and show, in particular, that $\lim_{r\to \infty} \frac{\log \kappa(n,r)}{r} = n-1$. Finally, we compare them with the numeric upper bounds obtained by solving a suitable semidefinite program. Comment: Will be merged with arXiv:1910.02715 |
| Databáze: | arXiv |
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