A Note on Minimal Translation Graphs in Euclidean Space

Dan Yang, Jingjing Zhang and Yu Fu
Additional contact information
Dan Yang: Normal School of Mathematics, Liaoning University, Shenyang 110044, China
Jingjing Zhang: Normal School of Mathematics, Liaoning University, Shenyang 110044, China
Yu Fu: School of Mathematics, Dongbei University of Finance and Economics, Dalian 116025, China

Mathematics, 2019, vol. 7, issue 10, 1-12

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/10/889/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/10/889/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:10:p:889-:d:270008

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().