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Siberian Mathematical Journal

, Volume 45, Issue 4, pp 628–645 | Cite as

Properties of the Mappings That Are Close to the Harmonic Mappings. II

  • A. P. Kopylov
Article

Abstract

We continue studying the mappings that are close to the harmonic mappings (ε-quasiharmonic mappings with ε small). This study originates with the previous articles of the author. The results of the article include a theorem on connection between the notion of ε-quasiharmonic mapping and the solutions to Beltrami systems, an analog to the arithmetic mean property of harmonic functions for ε-quasiharmonic mappings, a theorem on stability in the Poisson formula for harmonic mappings in the ball, and a theorem on the local smoothing of ε-quasiharmonic mappings with ε small which preserves proximity to the harmonic mappings.

stability of classes of harmonic mappings quasiharmonic mappings arithmetic mean property Poisson formula regularization 

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Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • A. P. Kopylov
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirsk

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