Quasi-symmetry without ratios
DOI:
https://doi.org/10.7146/math.scand.a-112190Abstract
We characterize quasi-symmetric maps between compact metric spaces as homeomorphisms uniformly at all scales.
References
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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
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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
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
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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
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