Lagrangian Mean Curvature Flows and Moment maps

Abstract

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.

34 pages, 1 figure; (ver. 2) The figure is fixed to be displayed correctly. Author's e-mail address is added.;(ver.3) A reference is added together with a related comment; (ver. 4) minor revision