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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.

• 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, ...

• 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, ...

• 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 ...