Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 287-304

DILATATIONS AND EXPONENTS OF QUASISYMMETRIC HOMEOMORPHISMS

Tao Cheng and Shanshuang Yang

East China Normal University, Department of Mathematics
Shanghai, 200241, P.R. China; tcheng 'at' math.ecnu.edu.cn

Emory University, Department of Mathematics and Computer Sciences
Atlanta, GA 30322, U.S.A.; syang 'at' mathcs.emory.edu

Abstract. Given a quasisymmetric homeomorphism, we introduce the concept of quasisymmetric exponent and explore its relations to other conformal invariants. As a consequence, we establish a necessary and sufficient condition on the equivalence of the dilatation and the maximal dilatation of a quasisymmetric homeomorphism by using the quasisymmetric exponent. A classification on the elements of the universal Teichmüller space is obtained by using this necessary and sufficient condition.

2010 Mathematics Subject Classification: Primary 30C62, 30C70.

Key words: Quasisymmetric homeomorphism, modulus, dilatation, quasisymmetric exponent.

Reference to this article: T. Cheng and S. Yang: Dilatations and exponents of quasisymmetric homeomorphisms. Ann. Acad. Sci. Fenn. Math. 41 (2016), 287-304.

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doi:10.5186/aasfm.2016.4122