Spaces and groups with conformal dimension greater than one

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.

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

References in corpus (2)

• Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary
• Existence of quasi-arcs

Cited by in corpus (3)

• Conformal dimension and random groups
• Hausdorff dimension of wiggly metric spaces
• On the Hausdorff dimension of the residual set of a packing by smooth curves