Duke Mathematical Journal

Spaces and groups with conformal dimension greater than one

John M. Mackay

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Abstract

We show that if a complete, doubling metric space is annularly linearly connected, then its conformal dimension is greater than one, quantitatively. As a consequence, we answer a question of Bonk and Kleiner: if the boundary of a one-ended hyperbolic group has no local cut points, then its conformal dimension is greater than one

Article information

Source
Duke Math. J. Volume 153, Number 2 (2010), 211-227.

Dates
First available in Project Euclid: 26 May 2010

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1274902080

Digital Object Identifier
doi:10.1215/00127094-2010-023

Mathematical Reviews number (MathSciNet)
MR2667133

Zentralblatt MATH identifier
1273.30056

Subjects
Primary: 51F99: None of the above, but in this section
Secondary: 20F67: Hyperbolic groups and nonpositively curved groups 30C65: Quasiconformal mappings in $R^n$ , other generalizations

Citation

Mackay, John M. Spaces and groups with conformal dimension greater than one. Duke Math. J. 153 (2010), no. 2, 211--227. doi:10.1215/00127094-2010-023. https://projecteuclid.org/euclid.dmj/1274902080


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