Calculus of Variations and Partial Differential Equations

, Volume 30, Issue 4, pp 513–522

The Dirichlet problem for constant mean curvature surfaces in Heisenberg space

  • Luis J. Alías
  • Marcos Dajczer
  • Harold Rosenberg
Original Article

DOI: 10.1007/s00526-007-0101-1

Cite this article as:
Alías, L.J., Dajczer, M. & Rosenberg, H. Calc. Var. (2007) 30: 513. doi:10.1007/s00526-007-0101-1

Abstract

We study constant mean curvature graphs in the Riemannian three- dimensional Heisenberg spaces \({\mathcal{H} = \mathcal{H}(\tau)}\) . Each such \({\mathcal{H}}\) 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 \({\mathcal{H}}\) with respect to the Riemannian submersion over certain domains \({\Omega \subset \mathbb{R}^2}\) taking on prescribed boundary values.

Mathematics Subject Classification (2000)

35J6053C42

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Luis J. Alías
    • 1
  • Marcos Dajczer
    • 2
  • Harold Rosenberg
    • 3
  1. 1.Departamento de MatematicasUniversidad de MurciaEspinardo, MurciaSpain
  2. 2.IMPARio de JaneiroBrazil
  3. 3.Département de MathématiquesUniversité de Paris VIIParisFrance