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The Great Picard theorem for quasiregular values
Abstract
We prove a version of Rickman's Great Picard theorem in the theory of quasiregular values. The version of the theorem that we prove is in fact stated in terms of omitted quasiregular values, unlike the previously known Little Picard theorem of the theory that is based on quasiregular values in the boundary of the image set. As a byproduct of the proof, we also prove a Riemann removability theorem in our setting, which ends up strengthening the conclusion of the previously resolved question of Astala, Iwaniec and Martin.
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BibTeX
@misc{kangasniemi2026great,
title = {{The Great Picard theorem for quasiregular values}},
author = {Ilmari Kangasniemi and Yizhe Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27976},
eprint = {2610.27976},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27976},
}
RIS
TY - UNPB
TI - The Great Picard theorem for quasiregular values
AU - Ilmari Kangasniemi
AU - Yizhe Zhu
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27976
UR - https://arxiv.org/abs/2610.27976
AB - We prove a version of Rickman's Great Picard theorem in the theory of quasiregular values. The version of the theorem that we prove is in fact stated in terms of omitted quasiregular values, unlike the previously known Little Picard theorem of the theory that is based on quasiregular values in the boundary of the image set. As a byproduct of the proof, we also prove a Riemann removability theorem in our setting, which ends up strengthening the conclusion of the previously resolved question of Astala, Iwaniec and Martin.
ER -