Examples of equivariant Lagrangian mean curvature flow

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.

arXiv comment8 pages, 7 figures. An abridged version will appear in Proceedings of the 2019 ISAAC Congress (Aveiro, Portugal)