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Doubling metric spaces are characterized by a lemma of Benjamini and Schramm


Author: James T. Gill
Journal: Proc. Amer. Math. Soc. 142 (2014), 4291-4295
MSC (2010): Primary 30L05; Secondary 28A75
DOI: https://doi.org/10.1090/S0002-9939-2014-12156-3
Published electronically: August 15, 2014
MathSciNet review: 3266996
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Abstract: A useful property of $ \mathbb{R}^n$ originally shown by I. Benjamini and O. Schramm turns out to characterize doubling metric spaces


References [Enhancements On Off] (What's this?)

  • [1] Patrice Assouad, Plongements lipschitziens dans $ {\bf R}^{n}$, Bull. Soc. Math. France 111 (1983), no. 4, 429-448 (French, with English summary). MR 763553 (86f:54050)
  • [2] Itai Benjamini and Nicolas Curien, On limits of graphs sphere packed in Euclidean space and applications, European J. Combin. 32 (2011), no. 7, 975-984. MR 2825530 (2012g:05050), https://doi.org/10.1016/j.ejc.2011.03.016
  • [3] Itai Benjamini and Oded Schramm, Recurrence of distributional limits of finite planar graphs, Electron. J. Probab. 6 (2001), no. 23, 13 pp. (electronic). MR 1873300 (2002m:82025), https://doi.org/10.1214/EJP.v6-96
  • [4] G. David and M. Snipes, A non-probabilistic proof of the Assouad embedding theorem with bounds on the dimension, Anal. Geom. Metr. Spaces 1 (2013), 36-41.MR 3108866
  • [5] Ori Gurel-Gurevich and Asaf Nachmias, Recurrence of planar graph limits, Ann. of Math. (2) 177 (2013), no. 2, 761-781. MR 3010812, https://doi.org/10.4007/annals.2013.177.2.10
  • [6] J. T. Gill and S. Rohde, On the Riemann surface type of random planar maps, Rev. Mat. Iberoam. 29 (2013), no. 3, 1071-1090, DOI 10.4171/RMI/749. MR 3090146
  • [7] Juha Heinonen, Lectures on analysis on metric spaces, Universitext, Springer-Verlag, New York, 2001. MR 1800917 (2002c:30028)
  • [8] Jouni Luukkainen, Assouad dimension: antifractal metrization, porous sets, and homogeneous measures, J. Korean Math. Soc. 35 (1998), no. 1, 23-76. MR 1608518 (99m:54023)
  • [9] John M. Mackay and Jeremy T. Tyson, Conformal dimension, Theory and application. University Lecture Series, vol. 54, American Mathematical Society, Providence, RI, 2010. MR 2662522 (2011d:30128)
  • [10] H. Namazi, P. Pankka and J. Souto, Distributional limits of Riemannian manifolds and graphs with sublinear genus growth, Geom. Funct. Anal. 24 (2014), no. 1, 322-359, DOI 10.1007/s00039-014-0259-6. MR 3177385
  • [11] Assaf Naor and Ofer Neiman, Assouad's theorem with dimension independent of the snowflaking, Rev. Mat. Iberoam. 28 (2012), no. 4, 1123-1142. MR 2990137, https://doi.org/10.4171/RMI/706

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Additional Information

James T. Gill
Affiliation: Department of Mathematics and Computer Science, Saint Louis University, 220 N. Grand Boulevard, St. Louis, Missouri 63103
Email: jgill5@slu.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12156-3
Keywords: Doubling space, Assouad dimension
Received by editor(s): November 14, 2012
Received by editor(s) in revised form: January 23, 2013, and January 28, 2013
Published electronically: August 15, 2014
Additional Notes: The author was supported by an NSF Mathematical Sciences Postdoctoral Research Fellowship DMS-1004721
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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