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- Title
Uniqueness of minimal surfaces whose boundary is a horizontal graph and some Bernstein problems in $${{\mathbb{H}^{2}\times \mathbb{R}}}$$.
- Authors
Sa Earp, Ricardo
- 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 $${{\mathbb{H}^{2}\times \mathbb{R}}}$$.
- Subjects
MINIMAL surfaces; PLATEAU'S problem; MAXIMA &; minima; MATHEMATICS; CURVES
- Publication
Mathematische Zeitschrift, 2013, Vol 273, Issue 1/2, p211
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-012-1001-4