Lack of Sphere Packing of Graphs via Non-Linear Potential Theory

Details Lack of Sphere Packing of Graphs via Non-Linear Potential Theory Lack of Sphere Packing of Graphs via Non-Linear Potential Theory

2009-10-16

arxiv.org/abs/0910.3071v2

Mathematics

Metric Geometry

10 pages

Scientific paper

It is shown that there is no quasi-sphere packing of the lattice grid Z^{d+1}
or a co-compact hyperbolic lattice of H^{d+1} or the 3-regular tree \times Z,
in R^d, 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.

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