Mean curvature flow of monotone Lagrangian submanifolds
The authors study the formation of singularities that monotone Lagrangian submanifolds in \({\mathbb C}^n\) develop under the mean curvature flow. In particular, they provide an estimate for the singular time in terms of the monotonicity constant of an embedded compact, oriented, monotone Lagrangian submanifold under the assumption that it remains embedded; and they provide results characterizing equality in this estimate. In the second part of the paper, the authors discuss equivariant Lagrangian submanifolds as a special case. They show that a certain class of embedded equivariant Lagrangian submanifolds is stable under the mean curvature flow and that both, type-1 as well as type-2 singularities occur within this class.
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