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Inventiones mathematicae

, Volume 120, Issue 1, pp 61–79 | Cite as

Definitions of quasiconformality

  • Juha Heinonen
  • Pekka Koskela
Article

Summary

We establish that the infinitesimal “H-definition” for quasiconformal mappings on Carnot groups implies global quasisymmetry, and hence the absolute continuity on almost all lines. Our method is new even inR n where we obtain that the “limsup” condition in theH-definition can be replaced by a “liminf” condition. This leads to a new removability result for (quasi)conformal mappings in Euclidean spaces. An application to parametrizations of chord-arc surfaces is also given.

Keywords

Euclidean Space Conformal Mapping Quasiconformal Mapping Absolute Continuity Carnot Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Juha Heinonen
    • 1
  • Pekka Koskela
    • 1
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

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