Lack of Sphere Packing of Graphs via Non-Linear Potential Theory
Abstract
It is shown that there is no quasi-sphere packing of the lattice grid Zd+1 or a co-compact hyperbolic lattice of Hd+1 or the 3-regular tree × Z, in Rd, for all d. A similar result is proved for some other graphs too. Rather than using a direct geometrical approach, the main tools we are using are from non-linear potential theory.
0