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Quasiregular Values and Rickman’s Picard Theorem

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Abstract

We prove a far-reaching generalization of Rickman’s Picard theorem for a surprisingly large class of mappings, based on the recently developed theory of quasiregular values. Our results are new even in the planar case.

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Acknowledgements

We thank Pekka Pankka for several helpful comments and insights on the paper. We also thank the anonymous referee for numerous suggested improvements that ended up significantly improving the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Cincinnati, P.O. Box 210025, Cincinnati, OH, 45221, USA

    Ilmari Kangasniemi

  2. Department of Mathematics, Syracuse University, Syracuse, NY, 13244, USA

    Jani Onninen

  3. Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), FI-40014, Jyväskylä, Finland

    Jani Onninen

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  1. Ilmari Kangasniemi
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  2. Jani Onninen
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Correspondence to Jani Onninen.

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I. Kangasniemi was supported by the National Science Foundation grant DMS-2247469. J. Onninen was supported by the National Science Foundation grant DMS-2154943.

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Kangasniemi, I., Onninen, J. Quasiregular Values and Rickman’s Picard Theorem. Geom. Funct. Anal. (2024). https://doi.org/10.1007/s00039-024-00674-x

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