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• The Hajłasz Capacity Density Condition is Self-improving 

  Canto, Javier; Vähäkangas, Antti V. (Springer Science and Business Media LLC, 2022)

  We prove a self-improvement property of a capacity density condition for a nonlocal Hajłasz gradient in complete geodesic spaces with a doubling measure. The proof relates the capacity density condition with boundary ...

• 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 ...

• 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, ...

• Approximation by uniform domains in doubling quasiconvex metric spaces 

  Rajala, Tapio (Springer, 2021)

  We show that any bounded domain in a doubling quasiconvex metric space can be approximated from inside and outside by uniform domains.