{
  "abstract": "A $λ$-translating soliton is a hypersurface in $\\mathbb{R}^{n+1}$ satisfying $H=\\langle \\mathbf{T},ν\\rangle+λ$; equivalently, it has constant weighted mean curvature with respect to the log-linear density $e^{\\langle T,X\\rangle}$, and is an eternal solution of the mean curvature flow with a constant forcing term. In this paper, we first prove that every complete properly immersed $λ$-translating soliton with $λ>0$ and $\\inf_ΣH>λ$ has at least exponential volume growth, in contrast with the linear growth of ordinary translating solitons. We then prove sharp non-existence results for graphic $λ$-translating solitons ($λ\\geqslant 0$) with bounded gradient, and two rigidity theorems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18064",
  "author_total": 2,
  "authors": [
    {
      "name": "Li Xiang"
    },
    {
      "name": "Sun Jun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/etydknfvtnqq2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18064",
  "fulltext_url": null,
  "id": "etydknfvtnqq2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18064",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7213520863",
  "pdf_url": "https://arxiv.org/pdf/2609.18064",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/etydknfvtnqq2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18064",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18064"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Rigidity and Non-existence Results of $λ$-Translating Solitons",
  "title_text": "Rigidity and Non-existence Results of λ-Translating Solitons",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/etydknfvtnqq2",
  "venue": "arXiv",
  "versions": []
}