Lagrangian mean curvature flow with boundary

Abstract

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

References in corpus (7)

• A canonical way to deform a Lagrangian submanifold
• Conjectures on Bridgeland stability for Fukaya categories of Calabi-Yau manifolds, special Lagrangians, and Lagrangian mean curvature flow
• Mean curvature flow of monotone Lagrangian submanifolds
• Evolution of networks with multiple junctions
• Lagrangian mean curvature flow of Whitney spheres
• Remarks on the self-shrinking Clifford torus
• Singularities of Equivariant Lagrangian Mean Curvature Flow

Cited by in corpus (2)

• Contracting convex surfaces by mean curvature flow with free boundary on convex barriers
• Curve shortening flow on Riemann surfaces with conical singularities