Singularities of Lagrange mean curvature flow: monotone case
The author studies the formation of singularities for the mean curvature flow of a monotone Lagrangian in \(\mathbb{C}^n\) with initial condition a Lagrangian in \(\mathbb{C}^n\) for which the Liouville class equals the Maslov class. He proves that if the singularity occurs before the critical time, then the tangent flow at the singularity can be decomposed into a finite union of area-minimizing Lagrangian cones (slag cones). When \(n=2\), he proves that each connected component of the rescaled flow converges to an area-minimizing cone (slag cone). Explicit examples in which such singularity formation occurs are also given.
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