A classification of minimal translation surfaces in Minkowski space

Volume 11, Issue 3, pp 437--443 http://dx.doi.org/10.22436/jnsa.011.03.12

Publication Date: February 28, 2018 Submission Date: July 06, 2017 Revision Date: December 31, 2017 Accteptance Date: January 07, 2018

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Authors

Dan Yang - School of Mathematics, Liaoning University, Shenyang, P. R. China. Wei Dan - School of Mathematics and Statistic, Guangdong University of Finance and Economics, Guangzhou, P. R. China. - Faculty of Arts and Sciences, Shenzhen Technology University, Shenzhen, P. R. China. Yu Fu - School of Mathematics, Dongbei University of Finance and Economics, Dalian, P. R. China.

Abstract

Minimal surfaces are well known as a class of surfaces with vanishing mean curvature which minimize area within a given boundary configuration since 19th century. This fact was implicitly proved by Lagrange for nonparametric surfaces in 1760, and then by Meusnier in 1776 who used the analytic expression for the mean curvature. Mathematically, a minimal surface corresponds to the solution of a nonlinear partial differential equation. By solving some differential equations, in this paper we give a complete and explicit classification of minimal translation surfaces in an \(n\)-dimensional Minkowski space.

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Keywords

• Minimal surfaces
• translation surfaces
• Minkowski space

MSC

•  53A10

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