Normality Criteria for Quasimeromorphic Mappings: Avoidance and Sharing
Abstract
We establish normality criteria for families of quasimeromorphic mappings in ℝn, n≥ 2, based on the avoidance and sharing of continuous functions. We first establish a rescaling principle for sequences of continuous functions and use it to derive a higher-dimensional analogue of Lappan's avoidance criterion. We then obtain normality criteria based on the sharing of continuous functions. In particular, we prove that a family of K-quasimeromorphic mappings sharing q0(n,K)+1 mutually disjoint continuous functions is normal, where q0(n,K) is the corresponding quasiregular Picard constant. We further consider sequences of quasimeromorphic mappings sharing sequences of continuous functions with a normal comparison sequence and establish a corresponding normality criterion, together with an improved bound under an additional separation condition on the limiting functions. Finally, we derive applications to normal quasiregular mappings into 𝕊n.
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BibTeX
@misc{datt2026normality,
title = {{Normality Criteria for Quasimeromorphic Mappings: Avoidance and Sharing}},
author = {Gopal Datt and Kushal Lalwani and Ashish Kumar Trivedi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.11791},
eprint = {2605.11791},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.11791},
}
RIS
TY - UNPB
TI - Normality Criteria for Quasimeromorphic Mappings: Avoidance and Sharing
AU - Gopal Datt
AU - Kushal Lalwani
AU - Ashish Kumar Trivedi
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2605.11791
UR - https://arxiv.org/abs/2605.11791
AB - We establish normality criteria for families of quasimeromorphic mappings in ℝ^n, n≥ 2, based on the avoidance and sharing of continuous functions. We first establish a rescaling principle for sequences of continuous functions and use it to derive a higher-dimensional analogue of Lappan's avoidance criterion. We then obtain normality criteria based on the sharing of continuous functions. In particular, we prove that a family of K-quasimeromorphic mappings sharing q_0(n,K)+1 mutually disjoint continuous functions is normal, where q_0(n,K) is the corresponding quasiregular Picard constant. We further consider sequences of quasimeromorphic mappings sharing sequences of continuous functions with a normal comparison sequence and establish a corresponding normality criterion, together with an improved bound under an additional separation condition on the limiting functions. Finally, we derive applications to normal quasiregular mappings into 𝕊^n.
ER -