{
  "abstract": "We study a positive radial graph evolving by $V=H^α+b$, with $α>0$ and $b<0$, in the unit cylinder and with $u_r(1,t)=u(1,t)$. We separate finite-time continuation estimates from the time-uniform interior estimates needed for convergence of normalized translates. On existing classical intervals we prove height and gradient bounds and an explicit conversion of velocity bounds into estimates for $H$, $u_r/r$, and $u_{rr}$. We derive the correct boundary defect for comparisons with finite-slope translators. Under independent interior velocity bounds and two-sided slope trapping, we prove compactness and identify every translated limit with the cup translator. We identify the radial zero-number comparison still required to establish that trapping. Stationary caps and power-law Robin laws are included.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08283",
  "author_total": 3,
  "authors": [
    {
      "name": "Tianhong Pu"
    },
    {
      "name": "Xiaoqian Xin"
    },
    {
      "name": "Lixia Yuan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/abdcac7m6xxpz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08283",
  "fulltext_url": null,
  "id": "abdcac7m6xxpz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08283",
  "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|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7220901330",
  "pdf_url": "https://arxiv.org/pdf/2610.08283",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/abdcac7m6xxpz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08283",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08283"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Radial Powered Mean Curvature Flow with Robin Boundary Conditions",
  "title_text": "Radial Powered Mean Curvature Flow with Robin Boundary Conditions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/abdcac7m6xxpz",
  "venue": "arXiv",
  "versions": []
}