Quasi-symmetry without ratios

  • Jaroslaw Kwapisz

Abstract

We characterize quasi-symmetric maps between compact metric spaces as homeomorphisms uniformly at all scales.

References

Graczyk, J. and Świątek, G., Smooth unimodal maps in the 1990s, Ergodic Theory Dynam. Systems 19 (1999), no. 2, 263–287. https://doi.org/10.1017/S014338579914286X

Heinonen, J., Lectures on analysis on metric spaces, Universitext, Springer-Verlag, New York, 2001. https://doi.org/10.1007/978-1-4613-0131-8

Herron, D. and Meyer, D., Quasicircles and bounded turning circles modulo bi-Lipschitz maps, Rev. Mat. Iberoam. 28 (2012), no. 3, 603–630. https://doi.org/10.4171/RMI/687

Mackay, J. M. and Tyson, J. T., Conformal dimension: Theory and application, University Lecture Series, vol. 54, American Mathematical Society, Providence, RI, 2010. https://doi.org/10.1090/ulect/054

Rohde, S., Quasicircles modulo bilipschitz maps, Rev. Mat. Iberoamericana 17 (2001), no. 3, 643–659. https://doi.org/10.4171/RMI/307

van Strien, S., One-dimensional dynamics in the new millennium, Discrete Contin. Dyn. Syst. 27 (2010), no. 2, 557–588. https://doi.org/10.3934/dcds.2010.27.557

Sullivan, D., Bounds, quadratic differentials, and renormalization conjectures, in “American Mathematical Society centennial publications, Vol. II (Providence, RI, 1988)'', Amer. Math. Soc., Providence, RI, 1992, pp. 417--466.

Tukia, P. and Väisälä, J., Quasisymmetric embeddings of metric spaces, Ann. Acad. Sci. Fenn. Ser. A I Math. 5 (1980), no. 1, 97–114. https://doi.org/10.5186/aasfm.1980.0531
Published
2019-08-29
How to Cite
Kwapisz, J. (2019). Quasi-symmetry without ratios. MATHEMATICA SCANDINAVICA, 125(1), 5-12. https://doi.org/10.7146/math.scand.a-112190
Section
Articles