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MiS Preprint

Longtime existence of the Lagrangian mean curvature flow

Knut Smoczyk


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.

MSC Codes:
lagrangian, mean curvature flow

Related publications

2004 Repository Open Access
Knut Smoczyk

Longtime existence of the Lagrangian mean curvature flow

In: Calculus of variations and partial differential equations, 20 (2004) 1, pp. 25-46