English

Triangular ratio metric in the unit disk

Metric Geometry 2021-03-09 v4

Abstract

The triangular ratio metric is studied in a domain GRnG\subsetneq\mathbb{R}^n, n2n\geq2. Several sharp bounds are proven for this metric, especially, in the case where the domain is the unit disk of the complex plane. The results are applied to study the H\"older continuity of quasiconformal mappings.

Keywords

Cite

@article{arxiv.2009.00265,
  title  = {Triangular ratio metric in the unit disk},
  author = {Oona Rainio and Matti Vuorinen},
  journal= {arXiv preprint arXiv:2009.00265},
  year   = {2021}
}

Comments

26 pages, 4 figures

R2 v1 2026-06-23T18:13:52.398Z