English

Remarks on the scale invariant Cassinian metric

Complex Variables 2020-07-07 v2

Abstract

We study the geometry of the scale invariant Cassinian metric and prove sharp comparison inequalities between this metric and the hyperbolic metric in the case when the domain is either the unit ball or the upper half space. We also prove sharp distortion inequalities for the scale invariant Cassinian metric under M\"obius transformations.

Keywords

Cite

@article{arxiv.1903.09099,
  title  = {Remarks on the scale invariant Cassinian metric},
  author = {Gendi Wang and Xiaoxue Xu and Matti Vuorinen},
  journal= {arXiv preprint arXiv:1903.09099},
  year   = {2020}
}

Comments

15 pages, 5 figures

R2 v1 2026-06-23T08:15:18.099Z