Longtime existence of the Lagrangian mean curvature flow

Knut Smoczyk
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Submission date: 20. Aug. 2002
published in: Calculus of variations and partial differential equations, 20 (2004) 1, p. 25-46 
MSC-Numbers: 53C44
Keywords and phrases: lagrangian, mean curvature flow

Abstract:
Given a compact Lagrangian submanifold in flat space evolving by its mean curvature, we prove uniform -bounds in space and -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.