Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



ACL homeomorphisms and linear dilatation

Authors: S. Kallunki and O. Martio
Journal: Proc. Amer. Math. Soc. 130 (2002), 1073-1078
MSC (2000): Primary 30C62, 30C65
Published electronically: September 14, 2001
MathSciNet review: 1873781
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We establish an integrability condition on the linear dilatation to guarantee ACL.

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

  • [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
  • [RR] Rado, T. and Reichelderfer, P.V., Continuous transformations in analysis, Die Grundlehren der matematischen Wissenschaften 75, Springer-Verlag, 1955. MR 18:115c
  • [T1] Tukia, P., Hausdorff dimension and quasisymmetric mappings, Math. Scand. 65 (1989), 152-160. MR 92b:30026
  • [T2] Tukia, P., Compactness properties of $\mu$-homeomorphisms, Ann. Acad. Sci. Fenn. Ser. AI Math. 16 (1991), 47-69. MR 93c:30029
  • [V] Väisälä, J., Lectures on $n$-dimensional quasiconformal mappings, Lecture Notes in Mathematics 229. Springer-Verlag, 1971. MR 56:12260

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 30C62, 30C65

Retrieve articles in all journals with MSC (2000): 30C62, 30C65

Additional Information

S. Kallunki
Affiliation: Department of Mathematics, University of Jyväskylä, P.O. Box 35, Fin-40351 Jyväskylä, Finland

O. Martio
Affiliation: Department of Mathematics, P.O. Box 4, FIN-00014 University of Helsinki, Finland

Received by editor(s): October 5, 2000
Published electronically: 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
Article copyright: © Copyright 2001 American Mathematical Society