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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
Posted:
February 18, 1999
MathSciNet review:
1610908
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Abstract: There is a quasiconformal mapping  of  to itself such that the image of  contains no rectifiable curves.
- 1.
Patrice
Assouad, Plongements lipschitziens dans 𝑅ⁿ,
Bull. Soc. Math. France 111 (1983), no. 4,
429–448 (French, with English summary). MR 763553
(86f:54050)
- 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
(95f:30031)
- 4.
P.
Tukia and J.
Väisälä, Quasisymmetric embeddings of metric
spaces, Ann. Acad. Sci. Fenn. Ser. A I Math. 5
(1980), no. 1, 97–114. MR 595180
(82g:30038)
- 1.
- Assouad, P. (1983) Prolongements Lipschitziens dans
 , Bull. Soc. Math. France 111, 429-448. MR 86f:54050
- 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.
- Heinonen, J. and Koskela, P. (1994) The boundary distortion of a quasiconformal mapping, Pacific J. Math 165, 93-114. MR 95f:30031
- 4.
- P. Tukia and J. Väisälä (1980) Quasisymmetric embeddings of metric spaces. Ann. Acad. Sci. Fenn. Ser. A I Math. 5, 97-114. MR 82g:30038
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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
Email:
bishop@math.sunysb.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-99-04900-X
PII:
S 0002-9939(99)04900-X
Keywords:
Quasisymmetric maps,
quasiconformal mappings,
rectifiable curves,
Jacobian
Received by editor(s):
September 22, 1997
Posted:
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
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