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ACL homeomorphisms and linear dilatation
Author(s):
S.
Kallunki;
O.
Martio
Journal:
Proc. Amer. Math. Soc.
130
(2002),
1073-1078.
MSC (2000):
Primary 30C62, 30C65
Posted:
September 14, 2001
MathSciNet review:
1873781
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Abstract:
We establish an integrability condition on the linear dilatation to guarantee ACL.
References:
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- [BA]
- Beurling, A. and Ahlfors, L.V., The boundary correspondence under quasiconformal mappings, Acta Math. 96 (1956), 125-142. MR 19:258c
- [FA]
- Fang Ainong, The ACL property of homeomorphisms under weak conditions, Acta Math. Sin., New Series 14.4 (1998), 473-480. MR 2000e:30035
- [G1]
- Gehring, F.W., The definitions and exceptional sets for quasiconformal mappings, Ann. Acad. Sci. Fenn. Ser. AI 281 (1960), 1-28. MR 23:A1800
- [G2]
- Gehring, F.W., Lower dimensional absolute continuity properties of quasiconformal mappings, Math. Proc. Camb. Phil. Soc. 78 (1975), 81-92. MR 52:3520
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- Tukia, P., Hausdorff dimension and quasisymmetric mappings, Math. Scand. 65 (1989), 152-160. MR 92b:30026
- [T2]
- Tukia, P., Compactness properties of
 -homeomorphisms, Ann. Acad. Sci. Fenn. Ser. AI Math. 16 (1991), 47-69. MR 93c:30029 - [V]
- Väisälä, J., Lectures on
 -dimensional quasiconformal mappings, Lecture Notes in Mathematics 229. Springer-Verlag, 1971. MR 56:12260
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Additional Information:
S.
Kallunki
Affiliation:
Department of Mathematics, University of Jyväskylä, P.O. Box 35, Fin-40351 Jyväskylä, Finland
Email:
sakallun@maths.jyu.fi
O.
Martio
Affiliation:
Department of Mathematics, P.O. Box 4, FIN-00014 University of Helsinki, Finland
Email:
olli.martio@helsinki.fi
DOI:
10.1090/S0002-9939-01-06265-7
PII:
S 0002-9939(01)06265-7
Received by editor(s):
October 5, 2000
Posted:
September 14, 2001
Additional Notes:
The first author was partially supported by the foundation Vilho, Yrjö ja Kalle Väisälän rahasto
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2001,
American Mathematical Society
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