{
  "abstract": "In this work, we establish existence and regularity results for solutions to nonlinear nonlocal equations of the form $f(Δ)u = U(x,u)$ and $f(Δ_{g})u = U(x,u)$ in Euclidean and Riemannian settings, respectively. We prove existence results across three distinct geometric scenarios: bounded domains in $\\mathbb{R}^n$, perturbed equations on compact Riemannian manifolds, and noncompact Cartan-Hadamard manifolds under suitable geometric curvature conditions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28572",
  "author_total": 1,
  "authors": [
    {
      "name": "Santiago Castellanos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b6s9c4e3a79s8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28572",
  "fulltext_url": null,
  "id": "b6s9c4e3a79s8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28572",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7223109296",
  "pdf_url": "https://arxiv.org/pdf/2610.28572",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b6s9c4e3a79s8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:22Z",
      "native_id": "2610.28572",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28572"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Nonlocal Equations on Domains and Manifolds Without Symmetries",
  "title_text": "Nonlocal Equations on Domains and Manifolds Without Symmetries",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/b6s9c4e3a79s8",
  "venue": "arXiv",
  "versions": []
}