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Lagrangian mean curvature flow and applications

PDE and Applied Math Seminar

Speaker: Adam Jacob, UC Davis
Location: 3106 MSB
Start time: Thu, Nov 21 2019, 4:30PM

Mean curvature flow is a natural parabolic flow on Riemannian submanifolds, with many important applications. Although most work related to the flow focuses on hypersurfaces, I will consider the case of a Lagrangian submanifold, which is a half dimensional submanifold where the restriction of a symplectic form vanishes. I will prove that, under certain bounded geometry assumptions, the Lagrangian mean curvature flow converges exponentially fast to an area minimizing submanifold. I will demonstrate how this can be applied to prove existence of special Lagrangian submanifolds on certain log Calabi-Yau manifolds, and how this leads to the existence of a special Lagrangian fibration in complex dimension 2. This is joint work with T.C. Collins and Y.-S. Lin.