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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Growth and isoperimetric profile of planar graphs
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by Itai Benjamini and Panos Papasoglu PDF
Proc. Amer. Math. Soc. 139 (2011), 4105-4111 Request permission

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 $|\partial \Omega | \precsim n$.
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Additional Information
  • Itai Benjamini
  • Affiliation: Department of Mathematics, Weizmann Institute, Rehovot, 76100, Israel
  • MR Author ID: 311800
  • 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
  • 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
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 4105-4111
  • MSC (2010): Primary 53C20, 53C23, 05C10
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10810-4
  • MathSciNet review: 2823055