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Quasispheres and metric doubling measures


Authors: Atte Lohvansuu, Kai Rajala and Martti Rasimus
Journal: Proc. Amer. Math. Soc. 146 (2018), 2973-2984
MSC (2010): Primary 30L10; Secondary 30C65, 28A75
DOI: https://doi.org/10.1090/proc/13971
Published electronically: April 4, 2018
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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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Additional Information

Atte Lohvansuu
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), FI-40014, University of Jyväskylä, Finland
Email: atte.s.lohvansuu@jyu.fi

Kai Rajala
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), FI-40014, University of Jyväskylä, Finland
Email: kai.i.rajala@jyu.fi

Martti Rasimus
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), FI-40014, University of Jyväskylä, Finland
Email: martti.i.rasimus@jyu.fi

DOI: https://doi.org/10.1090/proc/13971
Received by editor(s): January 23, 2017
Received by editor(s) in revised form: September 20, 2017
Published electronically: April 4, 2018
Additional Notes: This research was supported by the Academy of Finland, project number 308659
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2018 American Mathematical Society

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