{
  "annotation_id": "1ea9ab01-29ca-4fb3-8bfe-50cb12a4bb76",
  "date_created": "2026-02-17T05:53:20.118000Z",
  "date_modified": "2026-02-17T05:53:20.118000Z",
  "file_hash": "0406b181d7e0d581cc998b271d3e915a7262b03cb76e08f0ded4d3b048d250f7",
  "private": false,
  "record": {
    "abstract": "We prove a quantitative rigidity result for almost constant mean curvature spheres in $\\mathbb{R}^3$. Under a sub--two--sphere Willmore bound and a small $L^2$--CMC defect, we show that an almost--CMC surface is close to the round sphere, with linear control of the $W^{2,2}$--distance of the parametrization and the $L^\\infty$--norm of the conformal factor. An analogous statement holds under an a priori area bound below that of two spheres.The proof relies on a linearized analysis around the sphere. A previously established qualitative rigidity result provides the initial closeness required to enter the perturbative regime. The estimate further extends to integral $2$--varifolds of unit density using known regularity and density results.",
    "arxiv_id": "2601.09457",
    "authors": [
      "Yuchen Bi",
      "Jie Zhou"
    ],
    "categories": [
      "math.DG"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "title": "Linear Quantitative Rigidity for Almost-CMC Surfaces",
    "url": "https://arxiv.org/abs/2601.09457",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "46d83362-c917-4395-b65f-6018e1ef3d93",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}