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MiS Preprint
71/2002
Longtime existence of the Lagrangian mean curvature flow
Knut Smoczyk
Abstract
Given a compact Lagrangian submanifold in flat space evolving by its mean curvature, we prove uniform $C^{2,\alpha}$-bounds in space and $C^2$-estimates in time for the underlying Monge-Ampère equation under weak and natural assumptions on the initial Lagrangian submanifold. This implies longtime existence and convergence of the Lagrangian mean curvature flow. In the $2$-dimensional case we can relax our assumptions and obtain two independent proofs for the same result.
