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Definitions of quasiconformality

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, 48109, Ann Arbor, MI, USA

    Juha Heinonen & Pekka Koskela

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  1. Juha Heinonen
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  2. Pekka Koskela
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Oblatum 25-IV-1994 & 9-VI-1994

Both authors supported in part by NSF. The first author also acknowledges the support of the Academy of Finland and the Sloan Foundation.

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Heinonen, J., Koskela, P. Definitions of quasiconformality. Invent Math 120, 61–79 (1995). https://doi.org/10.1007/BF01241122

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