Mathematics Colloquia and Seminars

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Given a complex manifold X, a totally real submanifold is a half dimensional submanifold whose tangent space contains no complex lines. Examples include Lagrangian submanifolds of Kahler manifolds, as well as small deformations of Lagrangians. In the case that X is a negatively curved Kahler-Einstein manifold or a Calabi-Yau, we demonstrate that the mean curvature flow on a totally real submanifold L will converge exponentially fast to a minimal Lagrangian submanifold, provided that the initial mean curvature vector of L, as well as the initial restriction of the Kahler form to L, are sufficiently small in the C^0 norm. This is joint work with Tristan Collins and Yu-Shen Lin.