Archive for Rational Mechanics and Analysis

, Volume 195, Issue 3, pp 899–921 | Cite as

Deformations of Annuli with Smallest Mean Distortion



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

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of HelsinkiHelsinkiFinland
  2. 2.Department of MathematicsSyracuse UniversitySyracuseUSA
  3. 3.Institute for Advanced StudyMassey UniversityPalmerston NorthNew Zealand

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