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April 2015 Hausdorff dimension of wiggly metric spaces
Jonas Azzam
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Ark. Mat. 53(1): 1-36 (April 2015). DOI: 10.1007/s11512-014-0197-4


For a compact connected set X, we define a quantity β′(x, r) that measures how close X may be approximated in a ball B(x, r) by a geodesic curve. We then show that there is c>0 so that if β′(x, r)> β>0 for all xX and r< r0, then $\operatorname{dim}X>1+c\beta^{2}$. This generalizes a theorem of Bishop and Jones and answers a question posed by Bishop and Tyson.

Funding Statement

The author was supported by the NSF grants RTG DMS 08-38212 and DMS-0856687.


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Jonas Azzam. "Hausdorff dimension of wiggly metric spaces." Ark. Mat. 53 (1) 1 - 36, April 2015.


Received: 29 March 2013; Published: April 2015
First available in Project Euclid: 30 January 2017

zbMATH: 1319.30050
MathSciNet: MR3319612
Digital Object Identifier: 10.1007/s11512-014-0197-4

Rights: 2014 © Institut Mittag-Leffler


Vol.53 • No. 1 • April 2015
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