{
  "abstract": "We establish normality criteria for families of quasimeromorphic mappings in \\(\\mathbb{R}^n\\), \\(n\\geq 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 \\(\\mathbb{S}^n\\).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.11791",
  "author_total": 3,
  "authors": [
    {
      "name": "Gopal Datt"
    },
    {
      "name": "Kushal Lalwani"
    },
    {
      "name": "Ashish Kumar Trivedi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b4dryaw07jgk9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.11791",
  "fulltext_url": null,
  "id": "b4dryaw07jgk9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.11791",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7161024496",
  "pdf_url": "https://arxiv.org/pdf/2605.11791",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b4dryaw07jgk9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2605.11791",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.11791"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Normality Criteria for Quasimeromorphic Mappings: Avoidance and Sharing",
  "title_text": "Normality Criteria for Quasimeromorphic Mappings: Avoidance and Sharing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/b4dryaw07jgk9",
  "venue": "arXiv",
  "versions": []
}