Growth and isoperimetric profile of planar graphs
Authors:
Itai Benjamini and Panos Papasoglu
Journal:
Proc. Amer. Math. Soc. 139 (2011), 41054111
MSC (2010):
Primary 53C20, 53C23, 05C10
Published electronically:
March 17, 2011
MathSciNet review:
2823055
Fulltext PDF
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Additional Information
Abstract: Let be a planar graph such that the volume function of satisfies for some constant . Then for every vertex of and , there is a domain such that , and .
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 O. Angel, Growth and percolation on the uniform infinite planar triangulation, Geometric and Functional Analysis 13, 935974 (2003). MR 2024412 (2005b:60015)
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 P. Papasoglu, Cheeger constants of surfaces and isoperimetric inequalities, Trans. Amer. Math. Soc. 361 (2009), 51395162. MR 2515806
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Additional Information
Itai Benjamini
Affiliation:
Department of Mathematics, Weizmann Institute, Rehovot, 76100, Israel
Email:
itai.benjamini@weizmann.ac.il
Panos Papasoglu
Affiliation:
Mathematical Institute, University of Oxford, 2429 St Giles’, Oxford, OX1 3LB, United Kingdom
Email:
papazoglou@maths.ox.ac.uk
DOI:
http://dx.doi.org/10.1090/S000299392011108104
Received by editor(s):
April 24, 2010
Received by editor(s) in revised form:
September 24, 2010
Published electronically:
March 17, 2011
Communicated by:
Jianguo Cao
Article copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
