A note on the evolution of the Whitney sphere along mean curvature flow

TL;DR

This paper investigates how Whitney spheres evolve under Lagrangian mean curvature flow, demonstrating finite-time collapse to a point and convergence of tangent flows to a doubled Lagrangian plane.

Contribution

It provides new insights into the finite-time singularity formation and tangent flow behavior of equivariant Lagrangian spheres under mean curvature flow.

Findings

Equivariant Lagrangian spheres collapse in finite time.

Tangent flows converge to a Lagrangian plane with multiplicity two.

The study advances understanding of singularity development in Lagrangian mean curvature flow.

Abstract

We study the evolution of the Whitney sphere along the Lagrangian mean curvature flow. We show that equivariant Lagrangian spheres in $\mathbb{C}^n$ satisfying mild geometric assumptions collapse to a point in finite time and the tangent flows converge to a Lagrangian plane with multiplicity two.