Artículo
The Bernstein problem for elliptic Weingarten multigraphs
Autor/es | Fernández Delgado, Isabel
Gálvez, José A. Mira, Pablo |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2020 |
Fecha de depósito | 2021-07-07 |
Publicado en |
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Resumen | We prove that any complete, uniformly ellipticWeingarten surface in Euclidean
3-space whose Gauss map image omits an open hemisphere is a cylinder or a plane. This
generalizes a classical theorem by Hoffman, Osserman and ... We prove that any complete, uniformly ellipticWeingarten surface in Euclidean 3-space whose Gauss map image omits an open hemisphere is a cylinder or a plane. This generalizes a classical theorem by Hoffman, Osserman and Schoen for constant mean curvature surfaces. In particular, this proves that planes are the only complete, uniformly elliptic Weingarten multigraphs. We also show that this result holds for a large class of non-uniformly elliptic Weingarten equations. In particular, this solves in the affirmative the Bernstein problem for entire graphs for that class of elliptic equations. |
Agencias financiadoras | Ministerio de Economía y Competitividad (MINECO). España |
Identificador del proyecto | MTM2016-80313-P |
Cita | Fernández Delgado, I., Gálvez, J.A. y Mira, P. (2020). The Bernstein problem for elliptic Weingarten multigraphs. ArXiv.org, arXiv:2004.08275v1, 1-24. |
Ficheros | Tamaño | Formato | Ver | Descripción |
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2004.08275v1.pdf | 1.279Mb | [PDF] | Ver/ | |