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• 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 ...

• 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 ...

• 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, ...

• 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, ...

• 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, ...