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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Growth and isoperimetric profile of planar graphs


Authors: Itai Benjamini and Panos Papasoglu
Journal: Proc. Amer. Math. Soc. 139 (2011), 4105-4111
MSC (2010): Primary 53C20, 53C23, 05C10
Published electronically: March 17, 2011
MathSciNet review: 2823055
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Abstract: Let $ \Gamma $ be a planar graph such that the volume function of $ \Gamma $ satisfies $ V(2n)\leq CV(n)$ for some constant $ C>0$. Then for every vertex $ v$ of $ \Gamma $ and $ n\in \mathbb{N}$, there is a domain $ \Omega $ such that $ B(v,n)\subset \Omega$, $ \partial \Omega \subset B(v, 6n)$ and $ \vert\partial\Omega \vert \precsim n$.


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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, 24-29 St Giles’, Oxford, OX1 3LB, United Kingdom
Email: papazoglou@maths.ox.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10810-4
PII: S 0002-9939(2011)10810-4
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.