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Quasisymmetric Koebe uniformization with weak metric doubling measures
Rajala, Kai; Rasimus, Martti (Duke University Press, 2021)We give a characterization of metric spaces quasisymmetrically equivalent to a finitely connected circle domain. This result generalizes the uniformization of Ahlfors 2-regular spaces by Merenkov and Wildrick. -
Singular quasisymmetric mappings in dimensions two and greater
Romney, Matthew (Academic Press, 2019)For all n ≥2, we construct a metric space (X, d)and a quasisymmetric mapping f:[0, 1]n→X with the property that f−1 is not absolutely continuous with respect to the Hausdorff n-measure on X. That is, there exists a Borel ... -
Quasiconformal Jordan Domains
Ikonen, Toni (Walter de Gruyter GmbH, 2021)We extend the classical Carathéodory extension theorem to quasiconformal Jordan domains (Y,dY). We say that a metric space (Y,dY) is a quasiconformal Jordan domain if the completion Y of (Y,dY) has finite Hausdor 2-measure, ... -
Quasispheres and metric doubling measures
Lohvansuu, Atte; Rajala, Kai; Rasimus, Martti (American Mathematical Society, 2018)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, ... -
On a class of singular measures satisfying a strong annular decay condition
Arroyo, Ángel; Llorente, José G. (American Mathematical Society, 2019)A metric measure space (X, d, t) is said to satisfy the strong annular decay condition if there is a constant C > 0 such that for each x E X and all 0 < r < R. If do., is the distance induced by the co -norm in RN, we ...