Abstract
We define a subclass of quasiregular curves, called signed quasiregular curves, which contains holomorphic curves and quasiregular mappings. As our main result, we prove a growth theorem of Bonk-Heinonen type for signed quasiregular curves. To obtain our main result, we prove that signed quasiregular curves satisfy a weak reverse Hölder inequality and that this weak reverse Hölder inequality implies the main result. Further, we prove a cohomological value distribution result for signed quasiregular curves by using our main result and equidistribution.
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Acknowledgements
The author thanks her thesis advisor Pekka Pankka for all his help improving the manuscript. The author would also like thank the referee for suggested improvements.
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This work was supported in part by the Academy of Finland project #332671
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Heikkilä, S. Signed quasiregular curves. JAMA 150, 37–55 (2023). https://doi.org/10.1007/s11854-023-0270-7
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DOI: https://doi.org/10.1007/s11854-023-0270-7