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A Note on Minimal Translation Graphs in Euclidean Space

Author

Listed:
  • 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)

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.

Suggested Citation

  • Dan Yang & Jingjing Zhang & Yu Fu, 2019. "A Note on Minimal Translation Graphs in Euclidean Space," Mathematics, MDPI, vol. 7(10), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:889-:d:270008
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