{
  "annotation_id": "60340951-4958-43c0-bde4-b3260c0218e4",
  "date_created": "2026-02-17T05:53:11.753000Z",
  "date_modified": "2026-02-17T05:53:11.753000Z",
  "file_hash": "3b960542fe7ae5c5978376f628d2216fed0c1931ed8eca8eeb51c8492761abc9",
  "private": false,
  "record": {
    "abstract": "After Chern\u0027s conjecture on the discreteness of the constant scalar curvatures of compact minimal submanifolds $M^n$ in unit spheres $\\mathbb{S}^{n+q}$, Z. Q. Lu proposed a conjecture regarding the second gap, based on his ingenious refinement of the known first gap theorem. This refinement unifies Simons\u0027 first gap theorem for hypersurfaces with the corresponding theorems for high-codimensional submanifolds established by Yau, Shen, Li and Li, among others. In this paper, for arbitrary codimension, we prove Lu\u0027s conjecture for minimal 2-spheres, and for any minimal surfaces under some slight inequality conditions about the normal scalar curvature.",
    "arxiv_id": "2601.07194",
    "authors": [
      "Weiran Ding",
      "Jianquan Ge",
      "Fagui Li",
      "Xize Yang"
    ],
    "categories": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Lu\u0027s conjecture for minimal surfaces",
    "url": "https://arxiv.org/abs/2601.07194",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fc764956-e37b-4000-b391-9ff4541d339b",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}