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<p>We consider mappings satisfying an upper bound for the distortion of families of paths. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit mapping for a sequence of mappings converging locally uniformly. We separately consider cases when mappings are defined in the Euclidean <i>n</i>-dimensional space and in a metric space.</p>

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On lower distance estimates of mappings in metric spaces

  • 期刊论文

  • 发表日期：

    2025年8月6日

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  • N. Ilkevych,
  • D. Romash,
  • E. Sevost’yanov

摘要

We consider mappings satisfying an upper bound for the distortion of families of paths. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit mapping for a sequence of mappings converging locally uniformly. We separately consider cases when mappings are defined in the Euclidean n-dimensional space and in a metric space.