Journal d'Analyse Mathématique

, Volume 113, Issue 1, pp 265–291

Modulus of curve families and extremality of spiral-stretch maps


    • Department of MathematicsUniversity of Bern
  • Katrin Fässler
    • Department of MathematicsUniversity of Bern
  • Ioannis D. Platis
    • Department of MathematicsUniversity of Crete

DOI: 10.1007/s11854-011-0007-x

Cite this article as:
Balogh, Z.M., Fässler, K. & Platis, I.D. JAMA (2011) 113: 265. doi:10.1007/s11854-011-0007-x


We develop a method using the modulus of curve families to study minimisation problems for the mean distortion functional in the class of finite distortion homeomorphisms. We apply our method to prove extremality of the spiral-stretch mappings defined on annuli in the complex plane. This generalises results of Gutlyanskiĭ and Martio [12] and Strebel [23].

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© Hebrew University Magnes Press 2011