Archive for Rational Mechanics and Analysis

, Volume 195, Issue 3, pp 899–921

Deformations of Annuli with Smallest Mean Distortion


  • K. Astala
    • Department of MathematicsUniversity of Helsinki
  • T. Iwaniec
    • Department of MathematicsSyracuse University
    • Institute for Advanced StudyMassey University

DOI: 10.1007/s00205-009-0231-z

Cite this article as:
Astala, K., Iwaniec, T. & Martin, G. Arch Rational Mech Anal (2010) 195: 899. doi:10.1007/s00205-009-0231-z


We determine the extremal mappings with smallest mean distortion for mappings of annuli. As a corollary, we find that the Nitsche harmonic maps are Dirichlet energy minimizers among all homeomorphisms \({h:{{\mathbb A}}(r, R) \to {{\mathbb A}}(r', R')}\) . However, outside the Nitsche range of the modulus of the annuli, within the class of homeomorphisms, no such energy minimizers exist. In this case we identify the BV-limits of minimizers.

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© Springer-Verlag 2009