# Lagrangian Mean Curvature Flows and Moment maps

## TL;DR

This paper constructs and analyzes examples of Lagrangian mean curvature flows in Calabi-Yau manifolds using moment maps, including solitons and singularity studies, advancing understanding of geometric flows in complex manifolds.

## Contribution

It introduces a method to generate Lagrangian mean curvature flow examples via moment maps, applicable to both flat and non-flat Calabi-Yau spaces, and investigates their singularities.

## Key findings

- Constructed Lagrangian self-shrinkers and solitons in Euclidean space.
- Extended the method to non-flat Calabi-Yau manifolds, including Ricci-flat ALE spaces.
- Analyzed singularities of the constructed flows.

## 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.