Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 51-59

SHARPNESS OF UNIFORM CONTINUITY OF QUASICONFORMAL MAPPINGS ONTO s-JOHN DOMAINS

Chang-Yu Guo and Pekka Koskela

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35, FI-40014 University of Jyväskylä, Finland; changyu.c.guo 'at' jyu.fi

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35, FI-40014 University of Jyväskylä, Finland; pkoskela 'at' maths.jyu.fi

Abstract. We show that a prediction in [8] is inaccurate by constructing quasiconformal mappings onto s-John domains so that the mappings fail to be uniformly continuous between natural distances. These examples also exhibit the sharpeness of the assumptions in [5].

2010 Mathematics Subject Classification: Primary 30C62, 30C65.

Key words: s-John domain, uniform continuity, quasiconformal mapping, internal diameter, internal metric.

Reference to this article: C.-Y. Guo and P. Koskela: Sharpness of uniform continuity of quasiconformal mappings onto s-John domains. Ann. Acad. Sci. Fenn. Math. 42 (2017), 51-59.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4202