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• Uniformization with Infinitesimally Metric Measures 

  Rajala, Kai; Rasimus, Martti; Romney, Matthew (Springer, 2021)

  We consider extensions of quasiconformal maps and the uniformization theorem to the setting of metric spaces X homeomorphic to R2R2. Given a measure μμ on such a space, we introduce μμ-quasiconformal maps f:X→R2f:X→R2, ...

• 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, ...

• 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 ...

• Weighted Hardy Spaces of Quasiconformal Mappings 

  Benedict, Sita; Koskela, Pekka; Li, Xining (Springer, 2022)

  We study the integral characterizations of weighted Hardy spaces of quasiconformal mappings on the n-dimensional unit ball using the weight (1−r)n−2+α. We extend the known results for univalent functions on the unit disk. ...

• Duality of moduli in regular toroidal metric spaces 

  Lohvansuu, Atte (Finnish Mathematical Society, 2021)

  We generalize a result of Freedman and He [4, Theorem 2.5], concerning the duality of moduli and capacities in solid tori, to sufficiently regular metric spaces. This is a continuation of the work of the author and Rajala ...