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A note on the unique extremality of spiral-stretch maps

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Journal d'Analyse Mathématique Aims and scope

Abstract

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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Acknowledgment

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

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Authors and Affiliations

  1. Department of Mathematics, Soochow University, Suzhou, 215006, P.R. China

    Xiaogao Feng

  2. College of Mathematics and Information, China West Normal University, Nanchong, 637002, P.R. China

    Xiaogao Feng

  3. Department of Mathematics, Soochow University, Suzhou, 215006, P.R. China

    Yun Hu & Yuliang Shen

Authors
  1. Xiaogao Feng
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  2. Yun Hu
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  3. Yuliang Shen
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Corresponding author

Correspondence to Yuliang Shen.

Additional information

Research supported by the National Natural Science Foundation of China and the Natural Science Foundation of Jiangsu Province.

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Feng, X., Hu, Y. & Shen, Y. A note on the unique extremality of spiral-stretch maps. JAMA 138, 465–472 (2019). https://doi.org/10.1007/s11854-019-0039-1

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  • DOI: https://doi.org/10.1007/s11854-019-0039-1

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