{
  "abstract": "For an oriented regular plane curve $γ$, define ${\\cal T}γ=γ+τ$, where $τ$ is its unit tangent. We construct a noncircular curve $Γ_0$ such that every iterate ${\\cal T}^nΓ_0$, $n\\geq0$, is a smooth embedded closed curve with everywhere positive curvature. This answers a question of Tabachnikov. The construction starts with a noncompact convex curve $C$, asymptotic at its two ends to parallel lines, satisfying ${\\cal T} C=C+(V,0)$ for some $V>0$. From $C$ we construct long closed convex curves. After matching perimeters, we compare each curve with a convex curve whose unit-tangent image is the next curve in the sequence. In suitable arclength coordinates, their curvature functions differ by an exponentially small amount in $L^1$. Uniform inverse estimates turn these approximate relations into an exact sequence $Γ_{n+1}={\\cal T}Γ_n$. Each $Γ_n$ lies in a strip of width bounded independently of $n$, whereas the radii of iterated circles tend to infinity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10796",
  "author_total": 1,
  "authors": [
    {
      "name": "Dean Matthew Menezes"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/01nrzbveh3fg9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10796",
  "fulltext_url": null,
  "id": "01nrzbveh3fg9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10796",
  "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.DG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7221130906",
  "pdf_url": "https://arxiv.org/pdf/2610.10796",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/01nrzbveh3fg9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.10796",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10796"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A noncircular oval with convex unit-tangent iterates",
  "title_text": "A noncircular oval with convex unit-tangent iterates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/01nrzbveh3fg9",
  "venue": "arXiv",
  "versions": []
}