Lagrangian mean curvature flow with boundary

We introduce Lagrangian mean curvature flow with boundary in Calabi–Yau manifolds by defining a natural mixed Dirichlet-Neumann condition, and prove that under this flow, the condition is preserved. also study detail of equivariant discs on Lawlor neck self-shrinking Clifford torus, demonstrate long-time existence convergence first instance rescaled second.