Lack of sphere packing of graphs via nonlinear potential theory

Itai Benjamini; Oded Schramm

doi:10.1142/S1793525313500039

Lack of sphere packing of graphs via nonlinear potential theory

Itai Benjamini, Oded Schramm

Department of Mathematics

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

It is shown that there is no quasi-sphere packing of the lattice grid I^d+1 or a co-compact hyperbolic lattice of ${\mathcal{H}} ^{d+1}$ or the 3-regular tree × in ^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 nonlinear potential theory.

Original language	English
Pages (from-to)	1-11
Number of pages	11
Journal	Journal of Topology and Analysis
Volume	5
Issue number	1
DOIs	https://doi.org/10.1142/S1793525313500039
State	Published - Mar 2013

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

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title = "Lack of sphere packing of graphs via nonlinear potential theory",

abstract = "It is shown that there is no quasi-sphere packing of the lattice grid Id+1 or a co-compact hyperbolic lattice of ${\mathcal{H}} ^{d+1}$ or the 3-regular tree × in 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 nonlinear potential theory.",

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Lack of sphere packing of graphs via nonlinear potential theory

Abstract

All Science Journal Classification (ASJC) codes

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