Preprint 71/2002

Longtime existence of the Lagrangian mean curvature flow

Knut Smoczyk

Contact the author: Please use for correspondence this email.
Submission date: 20. Aug. 2002
published in: Calculus of variations and partial differential equations, 20 (2004) 1, p. 25-46 
DOI number (of the published article): 10.1007/s00526-003-0226-9
MSC-Numbers: 53C44
Keywords and phrases: lagrangian, mean curvature flow

Given a compact Lagrangian submanifold in flat space evolving by its mean curvature, we prove uniform formula4-bounds in space and formula6-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.

03.07.2017, 01:40