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Mappings of finite distortion: The Rickman-Picard theorem for mappings of finite lower order

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Abstract

We show that an entire mappingf of finite distortion with finite lower order can omit at most finitely many points when the distortion function off is suitably controlled. The proof uses the recently established modulus inequalities for mappings of finite distortion [15] and comparison inequalities for the averages of the counting function. A similar technique also gives growth estimates for mappings having asymptotic values.

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  1. Department of Mathematics and Statistics University of Jyväskylä, University of Jyväskylä, P.O. Box 35 (MAD), FIN-40014, Finland

    Kai Rajala

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  1. Kai Rajala
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Rajala, K. Mappings of finite distortion: The Rickman-Picard theorem for mappings of finite lower order. J. Anal. Math. 94, 235–248 (2004). https://doi.org/10.1007/BF02789048

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  • DOI: https://doi.org/10.1007/BF02789048

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