{
  "abstract": "Let $M$ be a smooth manifold and $TM$ its tangent bundle. A $C^0$-Finsler structure of $M$ is a continuous function $F: TM \\to [0, \\infty)$ such that restricted to each tangent space is an asymmetric norm. A mollifier smoothing of $F$ is a family of Finsler structures $F_\\varepsilon: TM \\to [0, \\infty)$, parameterized by $\\varepsilon > 0$ and constructed using the standard mollifier, such that $F_\\varepsilon \\to F$ uniformly on compact subsets as $\\varepsilon \\to 0$. In this work, we construct two mollifier smoothings of $F$. In the first, we assume that $F: TM \\to [0, \\infty)$ is strongly convex, that is, that $F$ restricted to each tangent space is strongly convex. In the second, we assume that $M=G$ is a Lie group and that $F:TG \\to [0, \\infty)$ is strongly convex and left-invariant, and in this case, $F_\\varepsilon$ is also left-invariant. In both cases, we prove that if $F$ is a Finsler structure, objects such as the fundamental tensor, the Chern, Cartan, Hashiguchi and Berwald connections, and the flag curvature of $(M, F_\\varepsilon)$ converge uniformly on compact subsets to the corresponding objects of $(M, F)$ as $\\varepsilon \\to 0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12108",
  "author_total": 2,
  "authors": [
    {
      "name": "Ryuichi Fukuoka"
    },
    {
      "name": "Anderson Macedo Setti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/52qcd5mbxxczx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12108",
  "fulltext_url": null,
  "id": "52qcd5mbxxczx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12108",
  "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": "W7221159084",
  "pdf_url": "https://arxiv.org/pdf/2610.12108",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/52qcd5mbxxczx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12108",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12108"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Mollifier smoothings of strongly convex $C^0$-Finsler structures",
  "title_text": "Mollifier smoothings of strongly convex C^0-Finsler structures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/52qcd5mbxxczx",
  "venue": "arXiv",
  "versions": []
}