Uniqueness of minimal surfaces whose boundary is a horizontal graph and some Bernstein problems in {{mathbb{H}^{2}times mathbb{R}}} |
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Authors: | Ricardo Sa Earp |
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Affiliation: | 1. Departamento de Matemática, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, RJ, 22453-900, Brazil
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Abstract: | We deduce that a connected compact immersed minimal surface in ${{mathbb{H}^{2}times mathbb{R}}}$ whose boundary has an injective horizontal projection on an admissible convex curve in ${partial_infty{mathbb{H}^{2}times mathbb{R}}}$ , and satisfies an admissible bounded slope condition, is the Morrey’s solution of the Plateau problem and is a horizontal minimal graph. We prove that there is no entire horizontal minimal graph in ${{mathbb{H}^{2}times mathbb{R}}}$ . |
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