Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 683-709

LIPSCHITZ CONDITIONS, TRIANGULAR RATIO METRIC, AND QUASICONFORMAL MAPPINGS

Jiaolong Chen, Parisa Hariri, Riku Klén and Matti Vuorinen

Hunan Normal University, Department of Mathematics
Changsha, P.R. China; jiaolongchen 'at' sina.com

University of Turku, Department of Mathematics and Statistics
20014 Turku, Finland; parisa.hariri 'at' utu.fi

Massey University, Auckland, New Zealand, and
University of Turku, Department of Mathematics and Statistics
20014 Turku, Finland; riku.klen 'at' utu.fi

University of Turku, Department of Mathematics and Statistics
20014 Turku, Finland; vuorinen 'at' utu.fi

Abstract. The triangular ratio metric is studied in subdomains of the complex plane and Euclidean n-space. Various inequalities are proven for this metric. The main results deal with the behavior of this metric under quasiconformal maps. We also study the smoothness of metric disks with small radii.

2010 Mathematics Subject Classification: Primary 51M10, 30C65.

Key words: Quasiconformal maps, quasiregular maps, conformal invariance, distortion theorem.

Reference to this article: J. Chen, P. Hariri, R. Klén and M. Vuorinen: Lipschitz conditions, triangular ratio metric, and quasiconformal maps. Ann. Acad. Sci. Fenn. Math. 40 (2015), 683-709.

Full document as PDF file

doi:10.5186/aasfm.2015.4039