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<p>We find a homeomorphism (or a sequence of homeomorphisms) with the smallest Lipschitz constant between two given Euclidean triangles (that is, acute triangles, right triangles, and obtuse triangles) with fixed area and we give a formula for the Lipschitz constant of this map. As applications of our results, we consider some special cases of the smallest Lipschitz constant between two quadrangles.</p>

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The optimal Lipschitz maps between Euclidean triangles

  • 期刊论文

  • 发表日期：

    2025年11月18日

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  • Xiaojun Hu,
  • Kejie Lin,
  • Peijia Liu,
  • Yonghu Zheng

摘要

We find a homeomorphism (or a sequence of homeomorphisms) with the smallest Lipschitz constant between two given Euclidean triangles (that is, acute triangles, right triangles, and obtuse triangles) with fixed area and we give a formula for the Lipschitz constant of this map. As applications of our results, we consider some special cases of the smallest Lipschitz constant between two quadrangles.