Quasispheres and metric doubling measures
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- by Atte Lohvansuu, Kai Rajala and Martti Rasimus PDF
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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.References
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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
- MR Author ID: 718650
- 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
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 2973-2984
- MSC (2010): Primary 30L10; Secondary 30C65, 28A75
- DOI: https://doi.org/10.1090/proc/13971
- MathSciNet review: 3787358