Lagrangian mean curvature flow of Whitney spheres

TL;DR

This paper demonstrates that Whitney spheres, as equivariant Lagrangian spheres with positive Ricci curvature, develop a specific type-II singularity under the mean curvature flow, which resembles a grim reaper solution.

Contribution

It establishes the development of type-II singularities for Whitney spheres under Lagrangian mean curvature flow, extending understanding of singularity formation in geometric flows.

Findings

Whitney spheres develop type-II singularities

Singularities resemble a grim reaper solution

Results apply to a class of equivariant Lagrangian spheres

Abstract

It is shown that an equivariant Lagrangian sphere with a positivity condition on its Ricci curvature develops a type-II singularity under the Lagrangian mean curvature flow that rescales to the product of a grim reaper with a flat Lagrangian subspace. In particular this result applies to the Whitney spheres.