English

Remarks on Martio's conjecture

Complex Variables 2021-06-03 v2

Abstract

We introduce a certain integrability condition for the reciprocal of the Jacobian determinant which guarantees the local homeomorphism property of quasiregular mappings with a small inner dilatation. This condition turns out to be sharp in the planar case. We also show that every branch point of a quasiregular mapping with a small inner dilatation is a Lebesgue point of the differential matrix of the mapping.

Keywords

Cite

@article{arxiv.2006.15101,
  title  = {Remarks on Martio's conjecture},
  author = {Ville Tengvall},
  journal= {arXiv preprint arXiv:2006.15101},
  year   = {2021}
}

Comments

15 pages, 0 figures

R2 v1 2026-06-23T16:39:23.049Z