{
  "abstract": "In this paper, we introduce the notation of stationary heat flow of $s$-harmonic maps from $\\R^m$ into the unit sphere $\\mathbb{S}^{\\ell-1}\\hookrightarrow \\mathbb{R}^\\ell$, for $0<s<1$, framed through the parabolic version of Caffarelli-Silvestre's extension. We prove that any stationary heat flow of $s$-harmonic maps is smooth away from a closed set of vanishing $(m+2-2s)$-dimensional parabolic Hausdorff measure. This extends to the fractional settings the partial regularity theorem on the heat flow of harmonic maps into spheres by Chen-Li-Lin and Feldman.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29191",
  "author_total": 4,
  "authors": [
    {
      "name": "Hengrong Du"
    },
    {
      "name": "Tao Huang"
    },
    {
      "name": "Armin Schikorra"
    },
    {
      "name": "Changyou Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5jhxq91yk98g3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29191",
  "fulltext_url": null,
  "id": "5jhxq91yk98g3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29191",
  "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.AP"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7223224035",
  "pdf_url": "https://arxiv.org/pdf/2610.29191",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5jhxq91yk98g3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29191",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29191"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Partial regularity of heat flow of fractional harmonic maps to spheres",
  "title_text": "Partial regularity of heat flow of fractional harmonic maps to spheres",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/5jhxq91yk98g3",
  "venue": "arXiv",
  "versions": []
}