{
  "abstract": "We present a new gradient-like flow that targets critical points of the inequality for the planar Radon transform $\\mathcal{R}$ proven by Oberlin and Stein, partially answering a question of Christ, who gave a complete characterisation of the extremisers of the inequality via rearrangement methods. We show that for non-negative radial initial data near the extremiser manifold, solutions to the flow exist globally and there exists a rescaled subsequence of the flow that converges to a critical point of the Radon functional $\\|\\mathcal{R} f\\|_3/\\|f\\|_{3/2}$ locally in $L^{3/2}(\\mathbb{R}^2)$. We also obtain a quantitative result for the rate of decay of critical points, which complements a result of Christ arXiv:1106.0719 in the special case of radial functions. We prove a novel localised smoothing estimate for the operator $\\mathcal{R}^*[(\\mathcal{R}\\cdot)^2]$ restricted to radial functions. This approach is complementary to that of Christ and provides a robust framework for studying extremal problems associated to Radon-like operators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39818",
  "author_total": 1,
  "authors": [
    {
      "name": "Yannis Galanos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4j59npdy9ar63.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39818",
  "fulltext_url": null,
  "id": "4j59npdy9ar63",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39818",
  "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"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.FA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39818",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4j59npdy9ar63.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39818",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39818"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Euler--Lagrange Flow Monotonicity for the Radon Transform",
  "title_text": "Euler--Lagrange Flow Monotonicity for the Radon Transform",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/4j59npdy9ar63",
  "venue": "arXiv",
  "versions": []
}