A Note on Minimal Translation Graphs in Euclidean Space

Abstract

In this note, we give a characterization of a class of minimal translation graphs generated by planar curves. Precisely, we prove that a hypersurface that can be written as the sum of n planar curves is either a hyperplane or a cylinder on the generalized Scherk surface. This result can be considered as a generalization of the results on minimal translation hypersurfaces due to Dillen−Verstraelen−Zafindratafa in 1991 and minimal translation surfaces due to Liu−Yu in 2013.

Keywords

• translation hypersurfaces
• minimal hypersurfaces
• Scherk surface