A Note on Minimal Translation Graphs in Euclidean Space

Mathematics

Dan Yang¹  Jingjing Zhang¹  Yu Fu² 

[1] Normal School of Mathematics, Liaoning University, Shenyang 110044, China;School of Mathematics, Dongbei University of Finance and Economics, Dalian 116025, China;

关键词: translation hypersurfaces;    minimal hypersurfaces;    Scherk surface;   

DOI  :  10.3390/math7100889

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown