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| Format: | Artículo científico |
| Language: | es |
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Escuela Regional de Matemáticas
2010
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| Online Access: | https://www.redalyc.org/articulo.oa?id=46817293003 |
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Table of Contents:
- El teorema clásico de Bernstein y algunos resultados de superficies de curvatura media constante en el espacio euclídeo S. Carolina García-Martínez Física, Astronomía y Matemáticas faces parabolicity entire graphs Euclidean space minimal surfaces The classical Bernstein theorem is one of the most important and celebrated results on global geometry of minimal surfaces. This result asserts that the planes are the only minimal surfaces of Euclidean space that can be written as the graph of a globally differentiable function defined on whole R2. In other words, the planes are the only entire minimal graphs in R3. The original proof of this result, given by Bernstein in [2, 3] is based in the theory of the partial differential equations. However, in this paper we present a proof more geometric following an approach given by S.S. Chern in [4]. Furthermore, we study some results of Klotz and Osserman [10] which characterize the complete constant mean curvature surfaces in Euclidean space whose Gaussian curvature does not change sign. 2010 artículo científico 0120-6788 https://www.redalyc.org/articulo.oa?id=46817293003 es http://www.redalyc.org/revista.oa?id=468 Matemáticas: Enseñanza Universitaria application/pdf Escuela Regional de Matemáticas Matemáticas: Enseñanza Universitaria (Colombia) Num.2 Vol.XVIII