Classification of Lagrangian translators and Lagrangian self-expanders in C^2

In this paper, we obtain several classification results of 2-dimensional complete Lagrangian translators and lagrangian self-expanders with constant squared norm |H|^2 of the mean curvature vector in C^2 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 -translators in C^2.