Abstract
The graph of a function f defined in some open set of the Euclidean space of dimension (p + q) is said to be a translation graph if f may be expressed as the sum of two independent functions ϕ and ψ defined in open sets of the Euclidean spaces of dimension p and q, respectively. We obtain a useful expression for the mean curvature of the graph of f in terms of the Laplacian, the gradient of ϕ and ψ as well as of the mean curvatures of their graphs. We study translation graphs having zero mean curvature, that is, minimal translation graphs, by imposing natural conditions on ϕ and ψ, like harmonicity, minimality and eikonality (constant norm of the gradient), giving several examples as well as characterization results.
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The first author was supported by the grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, Project No. PN-II-RU-TE-2011-3-0017. He would like also to thank UNAM for the warm hospitality during his visit in November 2013. The second author was partially supported by DGAPA-UNAM-PAPIIT, under Project IN113713-3 and thanks for the hospitality of both the Technical University Gh. Asachi and Al. I. Cuza University during his visit to Iaşi in May 2014. The third named author was partially supported by DGAPA-UNAM-PAPIIT, under Project IN100414.
An erratum to this article can be found at http://dx.doi.org/10.1007/s00009-016-0795-4.
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Munteanu, M.I., Palmas, O. & Ruiz-Hernández, G. Minimal Translation Hypersurfaces in Euclidean Space. Mediterr. J. Math. 13, 2659–2676 (2016). https://doi.org/10.1007/s00009-015-0645-9
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DOI: https://doi.org/10.1007/s00009-015-0645-9