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In this work we find all helicoidal surfaces in Minkowski space with constantmean curvature whose generating curve is a the graph of a polynomial or aLorentzian circle. In the first case, we prove that the degree of thepolynomial is $0$ or $1$ and that the surface is ruled. If the generating curveis a Lorentzian circle, we show that the only possibility is that the axis isspacelike and the center of the circle lies in the axis.

Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature