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

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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.

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  1. Sobolev Institute of Mathematics, Novosibirsk

    A. P. Kopylov

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Kopylov, A.P. Properties of the Mappings That Are Close to the Harmonic Mappings. II. Siberian Mathematical Journal 45, 628–645 (2004). https://doi.org/10.1023/B:SIMJ.0000035829.53352.67

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  • DOI: https://doi.org/10.1023/B:SIMJ.0000035829.53352.67

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