On singularities of mappings with a finite length distortion
Complex Variables
2025-11-04 v1
Abstract
We study the possibility of a continuous extension of a class of mappings to an isolated point on the boundary of a domain. We show that if some characteristic of this mapping is integrable on almost all spheres in the neighborhood of at least one point of the corresponding cluster set, then this mapping has a continuous extension to the specified point. In particular, this assertion is true if the specified characteristic is simply Lebesgue integrable in the neighborhood of at least one limit point.
Keywords
Cite
@article{arxiv.2511.01123,
title = {On singularities of mappings with a finite length distortion},
author = {Victoria Desyatka and Evgeny Sevost'yanov},
journal= {arXiv preprint arXiv:2511.01123},
year = {2025}
}