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A quasisymmetric surface
with no rectifiable curves

Author: Christopher J. Bishop
Journal: Proc. Amer. Math. Soc. 127 (1999), 2035-2040
MSC (1991): Primary 30C65
Published electronically: February 18, 1999
MathSciNet review: 1610908
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

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  • 2. Heinonen, J. and Semmes, S. (1997) Thirty-three yes or no questions about mappings, measures and metrics, Conf. Geometry and Dynamics 1, 1-12. CMP 97:13
  • 3. Juha Heinonen and Pekka Koskela, The boundary distortion of a quasiconformal mapping, Pacific J. Math. 165 (1994), no. 1, 93–114. MR 1285566
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Additional Information

Christopher J. Bishop
Affiliation: Department of Mathematics, State University of New York at Stony Brook, Stony Brook, New York 11794-3651

Keywords: Quasisymmetric maps, quasiconformal mappings, rectifiable curves, Jacobian
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
Article copyright: © Copyright 1999 American Mathematical Society