{
  "abstract": "We study bubbling for sequences of solutions of the Hamiltonian-perturbed Fueter equation. By Walpuski's compactness theorem, a bounded-energy sequence converges weakly to a Fueter map, with energy loss recorded by a defect measure supported on a codimension 2 rectifiable set. Assuming that the limiting map has no non-removable singularities and the bubbles attach to it on a subset of the bubbling locus of positive measure, we show that the limiting Hamiltonian lies in an exceptional subset of infinite codimension. The proof combines quantitative control of rational sweepout loci in hyperkähler manifolds with a transversality argument. We expect the attachment assumption to be automatic and follow from a suitable no-neck result. This strongly suggests that, in the absence of non-removable singularities, bubbling of Hamiltonian-perturbed Fueter maps is highly nongeneric.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.26803",
  "author_total": 1,
  "authors": [
    {
      "name": "Jacek Rzemieniecki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dkm24gj4881d3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.26803",
  "fulltext_url": null,
  "id": "dkm24gj4881d3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.26803",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7204526800",
  "pdf_url": "https://arxiv.org/pdf/2608.26803",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dkm24gj4881d3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2608.26803",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.26803"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On bubbling of Fueter maps",
  "title_text": "On bubbling of Fueter maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/dkm24gj4881d3",
  "venue": "arXiv",
  "versions": []
}