{
  "id": "1903.05785",
  "version": "v1",
  "published": "2019-03-14T01:23:18.000Z",
  "updated": "2019-03-14T01:23:18.000Z",
  "title": "Rigidity of Area-Minimizing $2$-Spheres in $n$-Manifolds with Positive Scalar Curvature",
  "authors": [
    "Jintian Zhu"
  ],
  "comment": "9 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We prove that the least area of the non-contractible immersed spheres is no more than $4\\pi$ in any oriented compact manifold with dimension $n+2\\leq 7$ which satisfies $R\\geq 2$ and admits a map to $\\mathbf S^2\\times T^n$ with nonzero degree. We also prove a rigidity result for the equality case. This can be viewed as a generalization of the result in [2] to higher dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-14T01:23:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C24",
      "53C42"
    ],
    "keywords": [
      "positive scalar curvature",
      "higher dimensions",
      "equality case",
      "rigidity result",
      "oriented compact manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}