Harmonic functions on planar and almost planar graphs and manifolds, via circle packings

Itai Benjamini; Oded Schramm

doi:10.1007/s002220050109

Harmonic functions on planar and almost planar graphs and manifolds, via circle packings

Inventiones mathematicae ◽

10.1007/s002220050109 ◽

1996 ◽

Vol 126 (3) ◽

pp. 565-587 ◽

Cited By ~ 30

Author(s):

Itai Benjamini ◽

Oded Schramm

Keyword(s):

Harmonic Functions ◽

Planar Graphs ◽

Circle Packings

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Circle Packings and Planar Graphs

Combinatorial Geometry ◽

10.1002/9781118033203.ch8 ◽

2011 ◽

pp. 95-113

Keyword(s):

Planar Graphs ◽

Circle Packings

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Boundaries of planar graphs, via circle packings

The Annals of Probability ◽

10.1214/15-aop1014 ◽

2016 ◽

Vol 44 (3) ◽

pp. 1956-1984 ◽

Cited By ~ 6

Author(s):

Omer Angel ◽

Martin T. Barlow ◽

Ori Gurel-Gurevich ◽

Asaf Nachmias

Keyword(s):

Planar Graphs ◽

Circle Packings

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Random walks and harmonic functions on infinite planar graphs

The Annals of Probability ◽

10.1214/aop/1065725179 ◽

1996 ◽

Vol 24 (3) ◽

pp. 1219-1238 ◽

Cited By ~ 16

Author(s):

Oded Schramm ◽

Itai Benjamini

Keyword(s):

Random Walks ◽

Harmonic Functions ◽

Planar Graphs ◽

Infinite Planar Graphs ◽

Infinite Planar

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Circle packings, kissing reflection groups and critically fixed anti-rational maps

Forum of Mathematics Sigma ◽

10.1017/fms.2021.81 ◽

2022 ◽

Vol 10 ◽

Author(s):

Russell Lodge ◽

Yusheng Luo ◽

Sabyasachi Mukherjee

Keyword(s):

Planar Graphs ◽

Rational Maps ◽

Reflection Groups ◽

Circle Packings

Abstract In this article, we establish an explicit correspondence between kissing reflection groups and critically fixed anti-rational maps. The correspondence, which is expressed using simple planar graphs, has several dynamical consequences. As an application of this correspondence, we give complete answers to geometric mating problems for critically fixed anti-rational maps.

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