{
  "abstract": "We study a nonlocal 2-Hessian equation, given by an infimum of linear deformations of the fractional Laplacian, that is, $\\inf_{A\\in {A}_2}Δ^s (u\\circ A)(A^{-1}x)$. We characterize the class of coefficient matrices ${A}_2$, which determines the behavior of the operator, and provide a detailed geometric description of the possible degeneracies. Our main theorem shows that the nonlocal 2-Hessian equation remains uniformly elliptic for strictly positive right-hand sides, which leads to regularity estimates. The results hold under weaker hypotheses than those previously considered in the literature, and for the full range $s\\in(0,1)$. In particular, no convexity on the solutions is required. Our hypotheses can be interpreted as nonlocal counterparts of the local notions of semiconcavity and 2-convexity. Moreover, all the results are stable as $s\\to1$, recovering the local case. The geometric methods developed here are new, even in the local setting, and may be relevant to a broader class of nonlocal fully nonlinear equations and curvature-type problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10195",
  "author_total": 3,
  "authors": [
    {
      "name": "Fernando Charro"
    },
    {
      "name": "María del Mar González"
    },
    {
      "name": "María Soria-Carro"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/anpjctw29bxqr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10195",
  "fulltext_url": null,
  "id": "anpjctw29bxqr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10195",
  "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.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7212160844",
  "pdf_url": "https://arxiv.org/pdf/2609.10195",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/anpjctw29bxqr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.10195",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10195"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A geometric approach to nonlocal 2-Hessian equations",
  "title_text": "A geometric approach to nonlocal 2-Hessian equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/anpjctw29bxqr",
  "venue": "arXiv",
  "versions": []
}