A kind of helicoidal surfaces in 3-dimensional Minkowski space

In this paper we constructed a helicoidal surface with a light-like axis with prescribed mean curvature or Gauss curvature given by smooth function in 3-dimensional Minkowski space E13 and solved an open problem left by Beneki, Kaimakamis, and Papantoniou in [J. Math. Anal. Appl. 275 (2002) 586-614].