{
  "id": "math/0612712",
  "version": "v1",
  "published": "2006-12-22T15:13:14.000Z",
  "updated": "2006-12-22T15:13:14.000Z",
  "title": "The Dirichlet problem for constant mean curvature surfaces in Heisenberg space",
  "authors": [
    "Luis J. Alias",
    "Marcos Dajczer",
    "Harold Rosenberg"
  ],
  "journal": "Calculus of Variations and PDE 30 (2007), 513--522",
  "doi": "10.1007/s00526-007-0101-1",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We study constant mean curvature graphs in the Riemannian 3-dimensional Heisenberg spaces ${\\cal H}={\\cal H}(\\tau)$. Each such ${\\cal H}$ is the total space of a Riemannian submersion onto the Euclidean plane $\\mathbb{R}^2$ with geodesic fibers the orbits of a Killing field. We prove the existence and uniqueness of CMC graphs in ${\\cal H}$ with respect to the Riemannian submersion over certain domains $\\Omega\\subset\\mathbb{R}^2$ taking on prescribed boundary values.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-12-22T15:13:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "53C42"
    ],
    "keywords": [
      "constant mean curvature surfaces",
      "heisenberg space",
      "dirichlet problem",
      "study constant mean curvature graphs",
      "riemannian submersion"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12712A"
    }
  }
}