{
  "id": "1912.07866",
  "version": "v1",
  "published": "2019-12-17T08:29:22.000Z",
  "updated": "2019-12-17T08:29:22.000Z",
  "title": "The Dirichlet problem of the constant mean curvature equation in Lorentz-Minkowski space and in Euclidean space",
  "authors": [
    "Rafael López"
  ],
  "comment": "Accepted in Mathematics, special volume Differential Geometry: Theory and Applications",
  "categories": [
    "math.DG"
  ],
  "abstract": "We investigate the differences and similarities of the Dirichlet problem of the mean curvature equation in the Euclidean space and in the Lorentz-Minkowski space. Although the solvability of the Dirichlet problem follows standards techniques of elliptic equations, we focus in showing how the spacelike condition in the Lorentz-Minkowski space allows to drop the hypothesis on the mean convexity which is required in the Euclidean case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-17T08:29:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58G20",
      "53A10",
      "53C50"
    ],
    "keywords": [
      "constant mean curvature equation",
      "dirichlet problem",
      "lorentz-minkowski space",
      "euclidean space",
      "euclidean case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}