{
  "id": "2103.10093",
  "version": "v1",
  "published": "2021-03-18T08:57:36.000Z",
  "updated": "2021-03-18T08:57:36.000Z",
  "title": "Conjectures on Convergence and Scalar Curvature",
  "authors": [
    "Christina Sormani",
    "Participants at the IAS Emerging Topics Workshop on Scalar Curvature",
    "Convergence"
  ],
  "comment": "Please email us any comments or corrections. 57 pages, 20 figures, IAS Emerging Topics on Scalar Curvature and Convergence",
  "categories": [
    "math.DG",
    "gr-qc",
    "math.MG"
  ],
  "abstract": "Here we survey the compactness and geometric stability conjectures formulated by the participants at the 2018 IAS Emerging Topics Workshop on {\\em Scalar Curvature and Convergence}. We have tried to survey all the progress towards these conjectures as well as related examples, although it is impossible to cover everything. We focus primarily on sequences of compact Riemannian manifolds with nonnegative scalar curvature and their limit spaces. Christina Sormani is grateful to have had the opportunity to write up our ideas and has done her best to credit everyone involved within the paper even though she is the only author listed above. In truth we are a team of over thirty people working together and apart on these deep questions and we welcome everyone who is interested in these conjectures to join us.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-18T08:57:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convergence",
      "geometric stability conjectures",
      "ias emerging topics workshop",
      "compact riemannian manifolds",
      "deep questions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}