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<p>We define linear and radial stretch maps in the affine-additive group, and prove that they are minimizers of the mean quasiconformal distortion functional. For the proofs we use a method based on the notion of modulus of a curve family and the minimal stretching property (MSP) of the afore-mentioned maps. MSP relies on certain given curve families compatible with the respective geometric settings of the stretch maps.</p>

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Stretch maps on the affine-additive group

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月25日

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  • Zoltán M. Balogh,
  • Elia Bubani,
  • Ioannis D. Platis

摘要

We define linear and radial stretch maps in the affine-additive group, and prove that they are minimizers of the mean quasiconformal distortion functional. For the proofs we use a method based on the notion of modulus of a curve family and the minimal stretching property (MSP) of the afore-mentioned maps. MSP relies on certain given curve families compatible with the respective geometric settings of the stretch maps.