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 \({\mathbb{R}^3}\) .
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Maria Fernanda Elbert was partially supported by CNPq and Faperj.
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Elbert, M.F., Rosenberg, H. Minimal graphs in \({M \times \mathbb{R}}\) . Ann Glob Anal Geom 34, 39–53 (2008). https://doi.org/10.1007/s10455-007-9096-2
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DOI: https://doi.org/10.1007/s10455-007-9096-2