{
  "abstract": "We study a linear boundary perturbation of the problem of prescribing the scalar curvature K and the boundary mean curvature H on a Riemannian manifold with umbilic boundary. Assuming that the Weyl tensor is nowhere vanishing along the boundary, we treat separately the cases in which K and H are constant and non-constant. In the negative scalar-curvature regime K<0, and in dimensions n≥8, we prove the existence of positive solutions that blow up at the boundary as the perturbation parameter tends to zero.",
  "abstract_shown": true,
  "affiliations": [
    "Dipartimento di Matematica, Universitá degli Studi di Bari Aldo Moro, 70125 Bari, Italy"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Giusi Vaira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5nevjshb3x59d.bib",
  "cited_by": 0,
  "doi": "10.3390/math14193555",
  "fulltext_url": null,
  "id": "5nevjshb3x59d",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/19/3555",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/5nevjshb3x59d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14193555",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/19/3555"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Blow-Up Phenomena for a Boundary Yamabe Problem with Umbilic Boundary",
  "title_text": "Blow-Up Phenomena for a Boundary Yamabe Problem with Umbilic Boundary",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/5nevjshb3x59d",
  "venue": "Mathematics",
  "versions": []
}