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)

 
 

 

A remark on the maximal dilatation of a quasiconformal mapping


Author: Matti Vuorinen
Journal: Proc. Amer. Math. Soc. 92 (1984), 505-508
MSC: Primary 30C60
DOI: https://doi.org/10.1090/S0002-9939-1984-0760934-6
MathSciNet review: 760934
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A lower bound for the maximal dilatation of a quasiconformal self-mapping of a uniform domain $ G$ in $ {R^n}$ with connected boundary is proved provided that the boundary is kept pointwise fixed by the mapping and that a prescribed point $ a$ is mapped on another point $ b$ in $ G$. The lower bound is given in terms of the quasihyperbolic distance from $ a$ to $ b$.


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

  • [1] G. D. Anderson and M. K. Vamanamurthy, An extremal displacement mapping in $ n$-space, Complex analysis, Joensuu, 1978, pp. 1-9; Lecture Notes in Math., vol. 747, Springer-Verlag, 1979. MR 553026 (81b:30030)
  • [2] F. W. Gehring and B. G. Osgood, Uniform domains and the quasihyperbolic metric, J. Analyse Math. 36 (1979), 50-74. MR 581801 (81k:30023)
  • [3] F. W. Gehring and B. P. Palka, Quasiconformally homogeneous domains, J. Analyse Math. 30 (1976), 172-199. MR 0437753 (55:10676)
  • [4] O. Martio and J. Sarvas, Injectivity theorems in plane and space, Ann. Acad. Sci. Fenn. Ser. A I Math. 4 (1978/1979), 383-402. MR 565886 (81i:30039)
  • [5] O. Teichmüller, Ein Verschiebungssatz der quasikonformen Abbildung, Deutsche Math. 7 (1944), 336-343. MR 0018761 (8:327b)
  • [6] J. Väisälä, Lectures on $ n$-dimensional quasiconformal mappings, Lecture Notes in Math., vol. 229, Springer-Verlag, 1971.
  • [7] M. Vuorinen, Conformal invariants and quasiregular mappings, in preparation.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30C60

Retrieve articles in all journals with MSC: 30C60


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0760934-6
Keywords: Quasiconformal mappings
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society