Minimal Translation Hypersurfaces in Euclidean Space
Minimal Translation Hypersurfaces in Euclidean Space
复制标题
DOI：
10.1007/s00009-015-0645-9
复制
发表时间：
2016-10
影响因子：
1.1
通讯作者：
M. Munteanu;O. Palmas;G. Ruiz-Hernández
中科院分区：
文献类型：
--
作者：
M. Munteanu;O. Palmas;G. Ruiz-Hernández
定义在(p+q)维欧氏空间的某个开集上的函数f的图形称为平移图，如果可以分别表示为定义在p+q维欧氏空间的开集上的两个独立函数ϕ和ψ的和。我们得到了图的平均曲率的拉普拉斯、ϕ和ψ的梯度以及它们的图的平均曲率的一个有用的表达式。研究了平均曲率为零的平移图，即极小平移图，通过在ϕ和ψ上施加调和性、极小性和eikonity(梯度的常模)等自然条件，给出了几个例子和刻画结果。
The graph of a functionfdefined in some open set of the Euclidean space of dimension (p+q) is said to be a translation graph iffmay be expressed as the sum of two independent functionsϕandψdefined in open sets of the Euclidean spaces of dimensionpandq, respectively. We obtain a useful expression for the mean curvature of the graph offin terms of the Laplacian, the gradient ofϕandψas 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 onϕandψ, like harmonicity, minimality and eikonality (constant norm of the gradient), giving several examples as well as characterization results.