{
  "id": "2106.15709",
  "version": "v1",
  "published": "2021-06-29T20:24:05.000Z",
  "updated": "2021-06-29T20:24:05.000Z",
  "title": "Metrics with $λ_1(-Δ+ k R) \\geq 0$ and flexibility in the Riemannian Penrose Inequality",
  "authors": [
    "Chao Li",
    "Christos Mantoulidis"
  ],
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "On a closed n-dimensional manifold, consider the space of all Riemannian metrics for which -Delta+kR is positive (nonnegative) definite, where k > 0 and R is the scalar curvature. This spectral generalization of positive (nonnegative) scalar curvature arises naturally for different values of $ in the study of scalar curvature in dimension n+1 via minimal hypersurfaces, the Yamabe problem in dimension n, and Perelman's surgery for Ricci flow in dimension n=3. We study these spaces in unison and generalize, as appropriate, positive scalar curvature results (Gromov--Lawson's codimension-3 surgery and Marques's connectedness) that we eventually apply to k = 1/2, where the space above models apparent horizons in (n+1)-dimensional time-symmetric initial data to the Einstein equations. Specifically, we compute the Bartnik mass (n=3) of apparent horizons and the Bartnik--Bray mass (n >= 2) of their outer-minimizing generalizations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-29T20:24:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemannian penrose inequality",
      "flexibility",
      "scalar curvature arises",
      "positive scalar curvature results",
      "models apparent horizons"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}