Quasispheres and metric doubling measures
Lohvansuu, A., Rajala, K., & Rasimus, M. (2018). Quasispheres and metric doubling measures. Proceedings of the American Mathematical Society, 146 (7), 2973-2984. doi:10.1090/proc/13971
Published inProceedings of the American Mathematical Society
© 2018 American Mathematical Society
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.