Spaces and groups with conformal dimension greater than one
Metric Geometry
2019-12-19 v2 Group Theory
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.
Cite
@article{arxiv.0711.0417,
title = {Spaces and groups with conformal dimension greater than one},
author = {John M. Mackay},
journal= {arXiv preprint arXiv:0711.0417},
year = {2019}
}
Comments
17 pages, 3 figures. v2: Final version, minor changes