English

On lower distance estimates of mappings in metric spaces

Complex Variables 2024-11-07 v1

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 nn-dimensional space and in a metric space.

Keywords

Cite

@article{arxiv.2411.03775,
  title  = {On lower distance estimates of mappings in metric spaces},
  author = {Evgeny Sevost'yanov and Denys Romash and Nataliya Ilkevych},
  journal= {arXiv preprint arXiv:2411.03775},
  year   = {2024}
}