A note on the unique extremality of spiral-stretch maps

  • Xiaogao Feng
  • Yun Hu
  • Yuliang ShenEmail author


In the recent paper [BFP], Balogh-Fässler-Platis proved that a spiral-stretch map is extremal for the extremal problem
$$\begin{array}{c}\rm{inf}\\ g\end{array}{\int\int_{A{_1}}}\frac{\varphi(K(w,g))}{|w|^2}dudv$$
among the set of all \(\mathbb{W}_{\rm{loc}}^{1,2}\)-homeomorphisms g with finite linear distortion K(w, g) between two annuli A1 and A2 and having the same boundary values with the spiral-stretch map. In this short note, we will give a very fast approach to this result without the \(\mathbb{W}_{\rm{loc}}^{1,2}\)-assumption. Furthermore, the unique extremality of a spiral-stretch map is also obtained.


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The authors would like to thank the referee for a very careful reading of the manuscript and for several corrections.


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© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  1. 1.Department of MathematicsSoochow UniversitySuzhouP.R. China
  2. 2.College of Mathmatics and InformationChina West Normal UniversityNanchongP.R. China
  3. 3.Department of MathematicsSoochow UniversitySuzhouP.R. China

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