Lagrangian mean curvature flows and moment maps

In this paper, we construct various examples of Lagrangian mean curvature flows in Calabi–Yau manifolds, using moment maps for actions of abelian Lie groups on them. The examples include Lagrangian self-shrinkers and translating solitons in the Euclidean spaces. Moreover, our method can be applied to construct examples of Lagrangian mean curvature flows in non-flat Calabi–Yau manifolds. In particular, we describe Lagrangian mean curvature flows in 4-dimensional Ricci-flat ALE spaces in detail and investigate their singularities.