Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 881-896

ON THE EXTENSION OF QUASISYMMETRIC MAPS

Pekka Alestalo and Dmitry Alexandrovich Trotsenko

Aalto University School of Science, Department of Mathematics and Systems Analysis
PL 11100, FI-00076 Aalto, Finland; pekka.alestalo 'at' aalto.fi

Sobolev Institute of Mathematics, Acad. Koptyug Avenue 4, 630090 Novosibirsk, Russia, and
Novosibirsk State University, Pirogova Street 2, 630090 Novosibirsk, Russia; trotsenk 'at' yandex.ru

Abstract. We show that an ε-power-quasisymmetric map f : A → Rⁿ can be extended to a Cε-power-quasisymmetric map F : Rⁿ → Rⁿ if A ⊂ Rⁿ satisfies a geometric thickness condition and ε is small enough. The constant C depends on c and n only.

2010 Mathematics Subject Classification: Primary 30C65, 46B20.

Key words: Power quasisymmetric, extension, sturdy.

Reference to this article: P. Alestalo and D.A. Trotsenko: On the extension of quasisymmetric maps. Ann. Acad. Sci. Fenn. Math. 41 (2016), 881-896.

Full document as PDF file

doi:10.5186/aasfm.2016.4154