Article
The Bernstein problem for elliptic Weingarten multigraphs
Author/s | Fernández Delgado, Isabel
Gálvez, José A. Mira, Pablo |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2020 |
Deposit Date | 2021-07-07 |
Published in |
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Abstract | 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. |
Funding agencies | Ministerio de Economía y Competitividad (MINECO). España |
Project ID. | MTM2016-80313-P |
Citation | Fernández Delgado, I., Gálvez, J.A. y Mira, P. (2020). The Bernstein problem for elliptic Weingarten multigraphs. ArXiv.org, arXiv:2004.08275v1, 1-24. |
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