{
  "annotation_id": "e947f669-3d8c-477f-a1d5-21b9b0b3b91f",
  "date_created": "2026-02-17T05:53:08.621000Z",
  "date_modified": "2026-02-17T05:53:08.621000Z",
  "file_hash": "caef180fb888a8bc8c28ffb66335ad7cf3b1e3abc0e97dcdb468059950d542b9",
  "private": false,
  "record": {
    "abstract": "Gromov conjectured that the total mean curvature of the boundary of a compact Riemannian manifold can be estimated from above by a constant depending only on the boundary metric and on a lower bound for the scalar curvature of the fill-in. We prove Gromov\u0027s conjecture if the manifolds are spin and the mean curvature is non-negative.",
    "arxiv_id": "2601.06713",
    "authors": [
      "Christian Baer"
    ],
    "categories": [
      "math.DG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Upper bound for the total mean curvature of spin fill-ins",
    "url": "https://arxiv.org/abs/2601.06713",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "20c80306-3ff4-4560-97ad-9fba9c584049",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}