Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 575-584

QUASISYMMETRIC EMBEDDING OF THE INTEGER SET AND ITS QUASICONFORMAL EXTENSION

Hiroki Fujino

Nagoya University, Graduate School of Mathematics
Furo-cho Chikusa-ku Nagoya 464-8602, Japan; m12040w 'at' math.nagoya-u.ac.jp

Abstract. We prove that an injection from the integer set into the real line admits a quasiconformal extension to the complex plane if and only if it is quasisymmetric.

2010 Mathematics Subject Classification: Primary 51M04; Secondary 51M05.

Key words: Quasiconformal mapping, quasisymmetric mapping.

Reference to this article: H. Fujino: Quasisymmetric embedding of the integer set and its quasiconformal extension. Ann. Acad. Sci. Fenn. Math. 42 (2017), 575-584.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4230