Examples of equivariant Lagrangian mean curvature flow

TL;DR

This paper presents key examples of Lagrangian mean curvature flow in complex two-space, highlighting invariant solutions, singularity formation, and important geometric objects, providing insights into both compact and non-compact cases.

Contribution

It offers a detailed exposition of explicit invariant examples of Lagrangian mean curvature flow, illustrating phenomena like singularities and long-time behavior in various geometric contexts.

Findings

Examples include Clifford and Chekanov tori, Whitney sphere, Lawlor necks.

Explicit models demonstrate singularity formation.

Analysis covers both compact and non-compact cases.

Abstract

In this expository note we describe important examples of Lagrangian mean curvature flow in $\mathbb{C}^2$ which are invariant under a circle action. Through these examples, we see compact and non-compact situations, long-time existence, singularities forming via explicit models, and significant objects in Riemannian and symplectic geometry, including the Clifford torus, Chekanov torus, Whitney sphere and Lawlor necks.