On lower distance estimates of mappings in metric spaces

Evgeny Sevost'yanov; Denys Romash; Nataliya Ilkevych

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arXiv · 2411.03775

On lower distance estimates of mappings in metric spaces

Evgeny Sevost'yanov·Denys Romash·Nataliya Ilkevych

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Abstract

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

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BibTeX RIS

Evgeny Sevost'yanov, Denys Romash, Nataliya Ilkevych. 2024-11-06. On lower distance estimates of mappings in metric spaces. https://arxiv.org/abs/2411.03775

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