49 citations · 218 across the 20 of their papers we have counts for
8 papers · 1 filter
Asymptotic dimension for covers with controlled growth
David Hume, John M. Mackay, Romain Tessera
We prove various obstructions to the existence of regular maps (or coarse embeddings) between commonly studied spaces. For instance, there is no regular map (or coarse embedding) $…
Conformal dimension of hyperbolic groups that split over elementary subgroups
Matias Carrasco, John M. Mackay
We study the (Ahlfors regular) conformal dimension of the boundary at infinity of Gromov hyperbolic groups which split over elementary subgroups. If such a group is not virtually f…
A Metrizable Topology on the Contracting Boundary of a Group
Christopher H. Cashen, John M. Mackay
The 'contracting boundary' of a proper geodesic metric space consists of equivalence classes of geodesic rays that behave like rays in a hyperbolic space. We introduce a geometrica…
Quasi-circles through prescribed points
John M. Mackay
We show that in an L-annularly linearly connected, N-doubling, complete metric space, any n points lie on a K-quasi-circle, where K depends only on L, N and n. This implies, for ex…
Modulus and Poincaré inequalities on non-self-similar Sierpinski carpets
John M. Mackay, Jeremy T. Tyson, Kevin Wildrick
A carpet is a metric space homeomorphic to the Sierpinski carpet. We characterize, within a certain class of examples, non-self-similar carpets supporting curve families of nontriv…
Assouad dimension of self-affine carpets
John M. Mackay
We calculate the Assouad dimension of the self-affine carpets of Bedford and McMullen, and of Lalley and Gatzouras. We also calculate the conformal Assouad dimension of those carpe…
Spaces and groups with conformal dimension greater than one
John M. Mackay
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 qu…
Existence of quasi-arcs
John M. Mackay
We show that doubling, linearly connected metric spaces are quasi-arc connected. This gives a new and short proof of a theorem of Tukia.