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<p>We study the asymptotic behavior of the diameter of image of a ball under ring <i>Q</i>-homeomorphisms with respect to the <i>p</i>-modulus for <i>p </i>&gt;<i> n</i> in the space ℝ<sup><i>n</i></sup><i>, n</i> ≥ 2. We also find the lower bound for the distortions of the diameter of ball image and solve extremal problems of minimization for the functionals of distortion of the diameter of ball image on some classes of ring <i>Q</i>-homeomorphisms with respect to the <i>p</i>-modulus.</p>

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On the Asymptotic Behavior of the Diameter of Image of a Ball at Infinity

  • 期刊论文

  • 发表日期：

    2025年10月28日

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  • Bogdan Klishchuk,
  • Ruslan Salimov,
  • Mariia Stefanchuk

摘要

We study the asymptotic behavior of the diameter of image of a ball under ring Q-homeomorphisms with respect to the p-modulus for p > n in the space ℝn, n ≥ 2. We also find the lower bound for the distortions of the diameter of ball image and solve extremal problems of minimization for the functionals of distortion of the diameter of ball image on some classes of ring Q-homeomorphisms with respect to the p-modulus.