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-Ampére 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.
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Received: 3 September 2002, Accepted: 12 June 2003, Published online: 4 September 2003
Mathematics Subject Classification (2000):
53C44
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Smoczyk, K. Longtime existence of the Lagrangian mean curvature flow. Cal Var 20, 25–46 (2004). https://doi.org/10.1007/s00526-003-0226-9
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DOI: https://doi.org/10.1007/s00526-003-0226-9