Quasispheres and metric doubling measures

Abstract

Applying the Bonk-Kleiner characterization of Ahlfors 2-regular quasispheres, we show that a metric two-sphere $X$ is a quasisphere if and only if $X$ is linearly locally connected and carries a weak metric doubling measure, i.e., a measure that deforms the metric on $X$ without much shrinking.

15 pages

References in corpus (2)

• Canonical parametrizations of metric discs
• Quasisymmetric spheres over Jordan domains