Quasispheres and metric doubling measures

2017/01/23 by Lohvansuu, Atte, Rajala, Kai, Rasimus, Martti · 1 citation
#28A75 (Secondary) #30C65 #30L10 (Primary) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1701.06345

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.

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