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• A Koebe distortion theorem for quasiconformal mappings in the Heisenberg group 

  Adamowicz, Tomasz; Fässler, Katrin; Warhurst, Ben (Springer, 2020)

  We prove a Koebe distortion theorem for the average derivative of a quasiconformal mapping between domains in the sub-Riemannian Heisenberg group H1. Several auxiliary properties of quasiconformal mappings between subdomains ...

• Conformality and Q-harmonicity in sub-Riemannian manifolds 

  Capogna, Luca; Citti, Giovanna; Le Donne, Enrico; Ottazzi, Alessandro (Elsevier Masson, 2019)

  We establish regularity of conformal maps between sub-Riemannian manifolds from regularity of Q-harmonic functions, and in particular we prove a Liouville-type theorem, i.e., 1-quasiconformal maps are smooth in all contact ...

• Mappings of generalized finite distortion and continuity 

  Doležalová, Anna; Kangasniemi, Ilmari; Onninen, Jani (Wiley-Blackwell, 2024)

  We study continuity properties of Sobolev mappings𝑓∈𝑊1,𝑛loc(Ω,ℝ𝑛),𝑛⩾2, that satisfy the following generalized finite distortion inequality||𝐷𝑓(𝑥)||𝑛⩽𝐾(𝑥)𝐽𝑓(𝑥) + Σ(𝑥)for almost every𝑥∈ℝ𝑛.Here𝐾∶ Ω→[1,∞)andΣ∶ ...

• Mappings of finite distortion : gauge dimension of generalized quasi-circles 

  Herron, D. A.; Koskela, Pekka (University of Illinois Press, 2003)

  We determine the correct dimension gauge for measuring generalized quasicircles (the images of a circle under so-called µ-homeomorphisms). We establish a sharp modulus of continuity estimate for the inverse of a homeomorphism ...

• Generalized dimension distortion under Sobolev mappings 

  Zapadinskaya, Aleksandra (University of Jyväskylä, 2011)