A doubling Loewner sphere that is not a quasisphere
arXiv:2609.16388
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.
arXiv comment15 pages, 2 figures