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A doubling Loewner sphere that is not a quasisphere
Abstract
We construct a metric 2-sphere of finite Hausdorff 2-measure that is doubling, linearly locally connected and Loewner but cannot be mapped to the standard sphere by a quasisymmetric mapping. Our result gives a negative answer to a question of Ntalampekos.
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BibTeX
@misc{romney2026doubling,
title = {{A doubling Loewner sphere that is not a quasisphere}},
author = {Matthew Romney},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16388},
eprint = {2609.16388},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16388},
}
RIS
TY - UNPB
TI - A doubling Loewner sphere that is not a quasisphere
AU - Matthew Romney
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.16388
UR - https://arxiv.org/abs/2609.16388
AB - We construct a metric 2-sphere of finite Hausdorff 2-measure that is doubling, linearly locally connected and Loewner but cannot be mapped to the standard sphere by a quasisymmetric mapping. Our result gives a negative answer to a question of Ntalampekos.
ER -