This paper provides upper and lower bounds on the kissing number of congruent radius $r > 0$ spheres in $mathbb{H}^n$, for $ngeq 2$. 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 $lim_{rto infty} frac{log kappa(n,r)}{r} = n-1$. Finally, we compare them with the numeric upper bounds obtained by solving a suitable semidefinite program.
تحميل البحث