Spaces and groups with conformal dimension greater than one

Details Spaces and groups with conformal dimension greater than one Spaces and groups with conformal dimension greater than one

2007-11-03

arxiv.org/abs/0711.0417v2

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

Mathematics

Metric Geometry

17 pages, 3 figures. v2: Final version, minor changes

Scientific paper

10.1215/00127094-2010-023

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.

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