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The core of this note is the observation that links between circle packings of graphs and potential theory developed in \cite{BeSc01} and \cite{HS} can be extended to higher dimensions.
The dissection of rectangles into squares
R. L. Brooks, C. A. B. Smith, A. H. Stone, and W. T. Tutte · 1940
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R. J. Duffin · 1962
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P. G. Doyle and J. L. Snell · 1984
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The convergence of circle packings to the riemann mapping
B. Rodin and D. Sullivan · 1987
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Square tilings with prescribed combinatorics
O. Schramm · 1993
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Parabolic index and rough isometries
P. M. Soardi and M. Yamasaki · 1993
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Average kissing numbers for non-congruent sphere packings
G. Kuperberg and O. Schramm · 1994
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Potential theory on infinite networks
P. M. Soardi · 1994
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A short proof that a subquadratic isoperimetric inequality implies a linear one
B. H. Bowditch · 1995
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Hyperbolic and parabolic packings
Z.-X. He and O. Schramm · 1995
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Random walks and harmonic functions on infinite planar graphs using square tilings
I. Benjamini and O. Schramm · 1996
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N. Alon. Packings with large minimum kissing numbers, Discrete Math
1997
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Introduction to circle packing
K. Stephenson · 2005
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Oded Schramm: From Circle Packing to SLE
S. Rohde · 2007
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On locally constructible spheres and balls
B. Benedetti and G. M. Ziegler · 2009
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Lack of sphere packings of graphs via non-linear potential theory
I. Benjamini and O. Schramm · 2009
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Acute triangulations of polyhedra and ℝ n \mathbb{R}^{n}
E. Kopczynski, I. Pak, and P. Przytycki · 2009
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Recurrence of distributional limits of finite planar graphs
I. Benjamini and O. Schramm · 2001
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J. Vasilis
Cited in the paper.
Random planar metrics
I. Benjamini · 2010
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