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Annals of Global Analysis and Geometry

, Volume 34, Issue 1, pp 39–53 | Cite as

Minimal graphs in \({M \times \mathbb{R}}\)

  • Maria Fernanda ElbertEmail author
  • Harold Rosenberg
Original Paper

Abstract

We study minimal graphs in \({M \times \mathbb{R}}\) . First, we establish some relations between the geometry of the domain and the existence of certain minimal graphs. We then discuss the problem of finding the maximal number of disjoint domains Ω ⊂ M that admit a minimal graph that vanishes on ∂Ω. When M is two-dimensional and has non-negative sectional curvature, we prove that this number is 3. This was proved by Tkachev in \({\mathbb{R}^3}\) .

Keywords

Minimal surface Minimal graph Unbounded domain 

Mathematics Subject Classification (2000)

53C42 

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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Instituto de MatematicaUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil
  2. 2.Institut de MathématiquesUniversité Paris VIIParisFrance

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