Lack of Sphere Packing of Graphs via Non-Linear Potential Theory
Metric Geometry
2010-11-16 v2 Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.0910.3071,
title = {Lack of Sphere Packing of Graphs via Non-Linear Potential Theory},
author = {Itai Benjamini and Oded Schramm},
journal= {arXiv preprint arXiv:0910.3071},
year = {2010}
}
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10 pages