Longtime existence of the Lagrangian mean curvature flow

Knut Smoczyk
May 2004
Calculus of Variations & Partial Differential Equations;May2004, Vol. 20 Issue 1, p25
Academic Journal
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-Amp�re 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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