{
  "abstract": "We study the solitons of the inverse curve shortening flow in the hyperbolic plane with respect to Killing fields: all parabolic fields, and the hyperbolic and elliptic fields with unit translation length and unit angular speed. The three cases reduce to one planar system. Except for a family of horocycles, every soliton has an endpoint at finite distance where the curvature blows up and the curve is a branch of a cusp. In the parabolic and elliptic cases there is a critical value $H$ of the parameter of the family: below $H$ the other end meets the ideal boundary orthogonally, above $H$ it is a second singular endpoint, and at $H$ the curvature tends to $1$. In the hyperbolic case $H=π/2$ and the critical solitons are horocycles. These horocycles are the only complete solitons and the only solitons of constant curvature.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.14385",
  "author_total": 2,
  "authors": [
    {
      "name": "Ivan Krznarić"
    },
    {
      "name": "Rafael López"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3rbxshfe8b2sr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.14385",
  "fulltext_url": null,
  "id": "3rbxshfe8b2sr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.14385",
  "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",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7161290727",
  "pdf_url": "https://arxiv.org/pdf/2605.14385",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3rbxshfe8b2sr.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2605.14385",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.14385"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Solitons for the inverse curve shortening flow on the hyperbolic plane",
  "title_text": "Solitons for the inverse curve shortening flow on the hyperbolic plane",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:42Z",
  "url": "https://research.draconitic.com/paper/3rbxshfe8b2sr",
  "venue": "arXiv",
  "versions": []
}