A quasisymmetric surface with no rectifiable curves
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- by Christopher J. Bishop
- Proc. Amer. Math. Soc. 127 (1999), 2035-2040
- DOI: https://doi.org/10.1090/S0002-9939-99-04900-X
- Published electronically: February 18, 1999
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Abstract:
There is a quasiconformal mapping $f$ of ${\Bbb R}^3$ to itself such that the image of ${\Bbb R}^2 \times \{0\}$ contains no rectifiable curves.References
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Bibliographic Information
- Christopher J. Bishop
- Affiliation: Department of Mathematics, State University of New York at Stony Brook, Stony Brook, New York 11794-3651
- MR Author ID: 37290
- Email: bishop@math.sunysb.edu
- Received by editor(s): September 22, 1997
- Published electronically: February 18, 1999
- Additional Notes: The author was supported in part by NSF grant # DMS 95-00577.
- Communicated by: Frederick W. Gehring
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2035-2040
- MSC (1991): Primary 30C65
- DOI: https://doi.org/10.1090/S0002-9939-99-04900-X
- MathSciNet review: 1610908