{
  "abstract": "We propose a thresholding scheme for the half-harmonic map heat flow from the flat torus $\\mathbb{T}^d$ into the unit sphere $\\mathbb{S}^m$ in $\\mathbb{R}^{m+1}$, whose iterates are given by convolution with the Poisson kernel, replacing the Gaussian kernel of the classical Merriman-Bence-Osher algorithm, and pointwise normalization. We prove that the piecewise constant interpolants subconverge to a weak solution of the half-harmonic maps heat flow that attains the initial map strongly in the energy space and satisfies the energy-dissipation inequality. For a spectrally truncated variant, convergence holds under a condition on the step size. A key ingredient is the derivation of the precise energy-dissipation identity directly from a refined within-step estimate, without resorting to De Giorgi interpolation typically used in the minimizing movement framework. This provides a direct way to recover the appropriate energy-dissipation property in the limit and, in turn, enables weak-strong uniqueness: every energy-dissipating weak solution coincides with the strong solution whenever the latter exists.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25912",
  "author_total": 3,
  "authors": [
    {
      "name": "Kilian Koch"
    },
    {
      "name": "Christof Melcher"
    },
    {
      "name": "Endre Süli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/637hv46fk4pc9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25912",
  "fulltext_url": null,
  "id": "637hv46fk4pc9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25912",
  "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": "W7214074061",
  "pdf_url": "https://arxiv.org/pdf/2609.25912",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/637hv46fk4pc9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25912",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25912"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Thresholding Scheme for the Half-Harmonic Map Heat Flow",
  "title_text": "Thresholding Scheme for the Half-Harmonic Map Heat Flow",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/637hv46fk4pc9",
  "venue": "arXiv",
  "versions": []
}