Classification of zero mean curvature surfaces of separable type in Lorentz-Minkowski space

Abstract

Consider the Lorentz-Minkowski 3-space L 3 with the metric dx 2 + dy 2 − dz 2 in canonical coordinates (x, y, z). A surface in L 3 is said to be separable if satisfies an equation of the form f (x) + g(y) + h(z) = 0 for some smooth functions f , g and h defined in open intervals of the real line. In this article we classify all zero mean curvature surfaces of separable type, providing a method of construction of examples.

On the minimality of quasi‐sum production models in microeconomics

“…Remark 3.3. Here, we use the similar technique developed in Kayar and López, 21 where the authors investigated zero mean curvature surfaces in 3-dimensional Lorentz-Minkowski space. With this method, one could construct many examples of minimal surfaces, which are of great interest to geometers.…”