Triangular ratio metric in the unit disk

: Rainio Oona, Vuorinen Matti

Publisher: Taylor & Francis Ltd

: 2022

: Complex Variables and Elliptic Equations

: COMPLEX VARIABLES AND ELLIPTIC EQUATIONS

: COMPLEX VAR ELLIPTIC

: 67

: 6

: 1299

: 1325

: 27

: 1747-6933

: 1747-6941

DOI: https://doi.org/10.1080/17476933.2020.1870452(external)

: https://doi.org/10.1080/17476933.2020.1870452(external)

: https://research.utu.fi/converis/portal/detail/Publication/53310663(external)

The triangular ratio metric is studied in a domain G subset of Rⁿ, n >= 2. 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 Holder continuity of quasiconformal mappings.

Triangular ratio metric in the unit disk.pdf