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Neck pinches in Lagrangian mean curvature flow

Jason Lotay

For a Lagrangian mean curvature flow which could converge to a special Lagrangian, the simplest singularities are modeled on special Lagrangians called Lawlor necks and are called neck pinches by Joyce. I will describe recent joint work with F. Schulze and G. Szekeleyhidi on Lagrangian surfaces, which shows that we can recognize a neck pinch using only information about the tangent flow at the singular time, that we can flow through the singularity and that there is a relation between the singularity formation and notions of stability.


Simons- Special Holonomy in Geometry, Analysis, and Physics: Progress and Open Problems