Classification of Lagrangian translators and Lagrangian self-expanders in C²

In this paper, we obtain several classification results of $2$-dimensional complete Lagrangian translators and lagrangian self-expanders with constant squared norm |H⃗|² of the mean curvature vector in C² by using a new Omori-Yau type maximum principle which was proved by Chen and Qiu {CQ}. The same idea is also used to give a similar result of Lagrangian ξ-translators in C².