{
  "annotation_id": "56e3f503-1935-4d16-abff-46f6bde82e0e",
  "date_created": "2026-02-17T05:53:15.701000Z",
  "date_modified": "2026-02-17T05:53:15.701000Z",
  "file_hash": "68701e038c95ea82d80f01f87e4b1668a9cd2e7cc8181ed87d1feeb7d783322f",
  "private": false,
  "record": {
    "abstract": "In this paper, we establish nonexistence results for complete translating solitons of the r-mean curvature flow under suitable growth conditions on the (r-1)-mean curvature and on the norm of the second fundamental form. We first show that such solitons cannot be entirely contained in the complement of a right rotational cone whose axis of symmetry is aligned with the translation direction. We then relax the growth condition on the (r-1)-mean curvature and prove that properly immersed translating solitons cannot be confined to certain half-spaces opposite to the translation direction. We conclude the paper by showing that complete, properly immersed translating solitons satisfying appropriate growth conditions on the (r-1)-mean curvature cannot lie completely within the intersection of two transversal vertical half-spaces.",
    "arxiv_id": "2601.08661",
    "authors": [
      "Hil\u00e1rio Alencar",
      "G. Pacelli Bessa",
      "Greg\u00f3rio Silva Neto"
    ],
    "categories": [
      "math.DG",
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Half-space theorems for translating solitons of the r-mean curvature flow",
    "url": "https://arxiv.org/abs/2601.08661",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "45663dc2-483a-4c13-bb9a-127efb978d47",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}