Lipschitz conditions, triangular ratio metric, and quasiconformal maps
Copyright policy )Lipschitz conditions, triangular ratio metric, and quasiconformal maps
The triangular ratio metric is studied in subdomains of the complex plane and Euclidean $n$-space. Various inequalities are proven for it. The main results deal with the behavior of this metric under quasiconformal maps. We also study the smoothness of metric disks with small radii.
30 pages, four figures
- TURUN YLIOPISTO Finland
- University of Turku Finland
- TURUN YLIOPISTO Finland
- Hunan Normal University China (People's Republic of)
- University of Turku Finland
51M10, 30C65, conformal invariance, Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations, Mathematics - Classical Analysis and ODEs, ta111, Classical Analysis and ODEs (math.CA), FOS: Mathematics, distortion theorem, quasiconformal maps, quasiregular maps
51M10, 30C65, conformal invariance, Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations, Mathematics - Classical Analysis and ODEs, ta111, Classical Analysis and ODEs (math.CA), FOS: Mathematics, distortion theorem, quasiconformal maps, quasiregular maps
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).32 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!