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

Itai Benjamini; Oded Schramm

REVIEW

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

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 0910.3071 v2 pith:DN7OYO2U submitted 2009-10-16 math.MG math.CO

Itai Benjamini , Oded Schramm This is my paper · ORCID

classification math.MGmath.CO

keywords graphslatticenon-linearpackingpotentialtheoryapproachco-compact

verification ladder T0 review T1 audit T2 compute T3 formal

0 comments

read the original 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.

Discussion (0). Continue with ORCID to comment.

Pith tools