Minimal graphs in {M times mathbb{R}} |
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Authors: | Maria Fernanda Elbert Harold Rosenberg |
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Affiliation: | (1) Instituto de Matematica, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil;(2) Institut de Mathématiques, Université Paris VII, Paris, France |
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Abstract: | We study minimal graphs in . 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 . Maria Fernanda Elbert was partially supported by CNPq and Faperj. |
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Keywords: | Minimal surface Minimal graph Unbounded domain |
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